Problems Involving Fundamental Counting Principle

1. Patrick wants to buy a computer system. In a computer shop, a customer can choose one of the 4 monitors, one of the 2 keyboards, one of the 4 CPU, and one of 3 printers. Determine the number of possible systems that Patrick can choose from.

2. An ice cream parlor is offering different flavors of ice cream with two kinds of containers available, cone and paper cup. The flavors of their ice cream include cheese, vanilla, mango, and chocolate. What is the total number of possible combinations if a customer can choose a container and 3 flavors of ice cream?

3. Emma has 5 blouses, 3 skirts, and 4 pairs of shoes. In how many different ways consisting of a blouse, a skirt, and a pair of shoes can Emma dress up?

4. Tess, Rina, Rose, Ronnie, Bryan, and Gab are all members of the Student Council. In how many ways can you form a committee of three students?

Problems Involving Probability of Simple Events

5. A letter is to be chosen from the letters of the word EXTRAVAGANT. What is the probability that it is a consonant?

6. An auditor of a club is to be selected from 8 Grade 7, 9 Grade 8, 12 Grade 9, and 5 Grade 10 students. What is the probability that he/she is not a Grade 8 student?

7. A spinner is divided into parts and whose colors are similar to a color wheel. What is the probability that the pointer lands on a secondary color?

8. Slips of paper are numbered 4, 5, 6, …, 34, folded into similar squares and placed in a bowl. If a paper is to be picked at random, what is the probability that the number is a prime number?

Answers

Answer 1

The questions are illustrations of combination and probability

Combination involves the ways of choosing or selecting an item from a group of itemsProbability involves the chance of choosing or selecting an item from a group of items

1. Number of systems to choose from

The given parameters are:

Monitors = 4

Keyboard = 2

CPU = 4

Printer = 3

The number of systems to choose from is:

n = 4 * 2 * 4 * 3 = 96

Hence, Patrick can choose from 96 systems

2. Combination of Ice cream

The given parameters are:

Containers = 2

Flavors = 4

The number of total combination to choose from is:

n = 2 * 4C3 = 8

Hence, the number of total combination is 8

3. Emma dressing up

The given parameters are:

Blouse = 5

Skirt = 3

Shoes = 4 pairc

The number of ways to dress up:

n = 5 * 3 * 4 = 60

Hence, Emma can dress up in 60 ways

4. Members of committee

The given parameters are:

Students = 6

Members of committee = 3

The number of ways to form a committee is:

n = 6C3 = 20

Hence, there are 20 ways to form the committee

5. Probability of consonant

We have:

Letters = 11

Consonnats = 7

The probability of selecting a consonant is:

P = 7/11

P = 0.636

Hence, the probability of selecting a consonant is: 0.636

6. Probability of not selecting a grade 8 student

We have:

Total students = 34

Students not in grade 8 = 25

The probability that a student is not in grade 8 is:

P = 25/34

P = 0.735

Hence, the probability that a student is not in grade 8 is 0.735

7. Probability of a secondary color

Not enough details to solve

8. Probability of a prime number

There are 9 prime numbers in a total number of 31 numbers from 4 to 34.

So, the probability that a number is prime is:

P = 9/31

P = 0.290

Hence, the probability that a number is prime is 0.290

Read more about combination and probability at:

https://brainly.com/question/24756209

https://brainly.com/question/11732255

Related Questions

a punch bowl contains 58 fluid ounces of fruit juice. Ishmat adds 2 containers of lemonade to the bowl. Each container holds 6 fluid ounces of lemonade.
How much liquid is in the punch bowl after Ishmat adds the lemonade?
46 fl oz
64 fl oz
66 fl oz
70 fl oz

Answers

Answer:

70 fl oz

Step-by-step explanation:

Find how much is added to the punch bowl.

2 containers and each holds 6 fluid ounces.

2 x 6 = 12

Now find the total amount of liquid by adding the original amount and the amount added.

58 + 12 = 70

Alberto’s monthly income is $3,200. Part of Alberto’s monthly budget is shown in the table.
Monthly Budget
Category Amount of Money
Rent $896
Groceries $384
Savings $165
Car payment $428
Utilities $120
What percentage of Alberto’s income is used to pay for his rent and groceries?

Answers

Using the percentage concept, it is found that 40% of Alberto’s income is used to pay for his rent and groceries.

What is a percentage?

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

[tex]P = \frac{a}{b} \times 100\%[/tex]

In this problem:

Alberto’s monthly income is $3,200, hence b = 3200.He spends 896 + 384 = $1280 in rent and groceries, hence a = 1280.

Then, the percentage is given by:

[tex]P = \frac{1280}{3200} \times 100\% = 40\%[/tex]

More can be learned about the percentage concept at https://brainly.com/question/10491646

A bond issued by ford on may 15, 1997 is scheduled to mature on may 15, 2097. if today is november 16, 2020, what is this bond's time to maturity?

Answers

The bond's time to maturity for the Ford bond based on the present date and the maturity date is 77 years 6 months.

What is the time to maturity?

The time to maturity for a bond is the length of time that a bondholder would receive interest payments on the bonds held. It is the difference between the present date and the matuity date of the bond.

Time to maturity = May 15 2097 - November 16, 2020 = 77 years 6 months

To learn more about bonds, please check: https://brainly.com/question/13326746

Find the slope of the line that is parallel and perpendicular to the following equation.
2x - y = 1

Answers

Answer:

Slope of the line that is parallel: 2

Slope of the line that is perpendicular: [tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

For the parallel line:

Rewrite your equation to slope-intercept form: y = mx + b

y = mx + b

m = slopeb = y-intercept (when x = 0)

2x - y = 1 <== subtract 2x to both sides

-2x -2x

-y = -2x + 1 <== divide both sides by -1

/-1 /-1

y = 2x - 1

The slope of the line that is parallel to this line is 2.

For the perpendicular line:

*Perpendicular lines have negative reciprocals*

Steps:

1. Take your original slope (2)

2. Flip it (1/2)

3. Change the sign (-1/2)

For a slope of 2, the reciprocal would be: [tex]-\frac{1}{2}[/tex]

Hope this helps!

Note that.

Slopes of parallel line are equal

Slopes of perpendicular lines are negative reciprocals

2x-y=1y=2x-1

Compare to slope intercept form

slope=m=2

Slope of the parallel line=2

Slope of the perpendicular line=-1/2

The table shows the possible outcomes of spinning the given spinner and tossing a fair coin. find the probability of spinning a 1 and tossing a head.

Answers

Considering a six-sided spinner, it is found that the probability of spinning a 1 and tossing a head is of [tex]\frac{1}{12}[/tex].

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem:

For the spinner, one is one out of six possible outcomes.For the coin, a head is one out of two possible outcomes.

Since the events are independent, the probability of spinning a 1 and tossing a head is given by:

[tex]p = \frac{1}{6} \times \frac{1}{2} = \frac{1}{12}[/tex].

More can be learned about probabilities at https://brainly.com/question/14398287

help me please i am so confused please

Answers

Answer: 75$

Step-by-step explanation:

1/4 is equal to 25/100.

meaning that 1/4 is 25 out of 100.

Based on that, if we subtract 25 from 100 we get 75.

Kevin is remodeling his bathroom. He needs to cut a circular hole out of a countertop to place the sink, as shown in the figure. What will be the area of the countertop once Kevin cuts the hole, to the nearest square inch? Use 3.14 as an approximation for pi.

Answers

Answer:

838 inches²

Step-by-step explanation:

Finding the area of the countertop including the hole

⇒ Area of countertop including hole: LB

⇒ Area of countertop including hole: (24)(48)

⇒ Area of countertop including hole: 1152 inches²

Finding the area of the hole (sink)

⇒ Area of hole: πr²

⇒ Area of hole: (π)(D/2)²

⇒ Area of hole: (π)(20/2)²

⇒ Area of hole: (π)(10)²

⇒ Area of hole: (π) x 100

⇒ Area of hole: 3.14 x 100 = 314 inches²

Finding the area excluding the hole

1152 - 314 = Area of countertop (excluding the hole)

838 inches² = Area of countertop (excluding the hole)

What is the measure of the missing angle?

Answers

hello! every triangle’s interior angles add up to 180. here would be how I solve this equation.

180-75-40=65 (find missing angle)
65+x=180 (supplementary angles)
180-65=x (substitution)
115=x (simplify)
x=115 (reflexive property of equality)

What is the area of the parallelogram if each square is 1 square foot?
12 ft
12
12 ft3
12ft2

Answers

To calculate the area of a parallelogram

⇒ we must know the formula

⇒ Area = base * height

What are we given:

Base length: it is 4ft because we counted that the length covered 4 squareHeight length: it is 3ft because we counted that the height covered 3 square

Thus:

Area = 3ft * 4ft = 12 [tex]ft^2[/tex]

Hope that helps!

What is 1748 divided by 38 can u show the work

Answers

Answer:

46

Explanation:

The given Divisor = 38 and Dividend = 1748

46
38|1748
152
228
- 228
0
The Quotient is 46 and the Remainder is 0

Please mark brainliest

Juanita a talented artist. She makes and sells t-shirts showing her art work.
She bought a silk screen machine for $400. The materials to make each shirt
cost her $ 8.00. If she sells her shirts for $28, how many shirts must she sell to
make a profit?

Answers

Answer:

answer 436 tubig is water halimaw is monster ang Ganda mo Sana kaso ang height mo pang kinder

Step-by-step explanation:

answer is 436 I hope it helps

f(x)=-3x-23
g(x)=3x+25
I need points X and y
I will give brainly

Answers

Answer:

refer to this image here:

hope this helps :)

We will use graphical way to solve it

y=-3x-23y=3x+25

Graph it

Solution is

(-8,1)

You are driving a 50 foot vehicle at night. although you are on the highway, a bad rainstorm is forcing you to creep along at 35 mph. you should keep ___seconds of distance between you and the vehicle ahead.

Answers

You should keep 0.97 seconds of distance between you and the vehicle ahead.

How to calculate the distance and time taken by a car

The formula for calculating distance is expressed as:

distance = speed * time

Time = Distance/Speed

Given the following parameters

Distance = 50 feet

Speed = 35mph = 51.3ft/s

Time taken = 50/51.3
Time taken = 0.97

Hence you should keep 0.97 seconds of distance between you and the vehicle ahead.

Learn more on distance and speed here: https://brainly.com/question/11495758

What is an equation of the line that passes through the points (4, 7) and (-3, 7)?

Answers

Step-by-step explanation:

Slope= 7-7/-3-4

0/-7

y-7 = 0(x-4)

y-7= 0

y=7

MARK ME AS BRAINLIST

5[tex]5x^{2} + 20x - 60 =[/tex]

Answers

Answer:

−

Factor

out of

−

Tap for more steps...

(

−

)

Factor.

Tap for more steps...

(

−

)

(

)

Step-by-step explanation:

ANSWER IS =5X2+20X-60

------------------------------

THIS ANSWER IS CORRECT

CHOOSING BRAINLIEST PLEASE HELP

Answers

Answer:

i think that the correct answer would be A or C

Step-by-step explanation:

hope this helps

sorry if the answers that i gave you is incorrect

Answer:

2nd option

Step-by-step explanation:

the nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 64 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{32}{64}[/tex] = [tex]\frac{1}{2}[/tex] , then

[tex]a_{n}[/tex] = 64 [tex](\frac{1}{2}) ^{n-1}[/tex]

what is the exact volume as x? (attached image)

Answers

Answer:

x = 25

Step-by-step explanation:

The 45-45-90 triangle is a special isoceles right triangle. If you look at the help image attached, you will see that it has the following rules:

a = xb = xc = x√2

Find x

c = x√2

25√2 = x√2

25√2 ÷ √2 = x

x = 25

I hope this helps!

What is the value of x? Enter your answer in the box.

x =

Answers

Answer: 12

Step-by-step explanation:

A straight line has a measurement of 180° so these two angles added together will equal 180°.

(10x - 20)° + (6x + 8)° = 180°

10x° + 6x° + 8° - 20° = 180°

16x° -12° = 180°

16x° = 192°

x = 12

Supplementary angles

10x-20+6x+8=18016x-12=18016x=180+1216x=192x=192/16x=12

Please help me and tysm!

Answers

Answer:

200

Step-by-step explanation:

156.7

since the number before the hundred is more than 4

it becomes 200

Help please!

Betty is 5 more than 3 times Jadyn's age. Betty is 41 old.
Write and solve an equation to find Jadyn's age, x

Equation:

Solution: x=

Jadyn is( ) years old.

Answers

Answer:

12 years old

Step-by-step explanation:

3x+5=41

3 times a number and 5 more

'more' usually means adding

41-5 =36

36/3 =12

Answer:

Equation: 41 = 3x + 5

x = 12

Step-by-step explanation:

Hello!

Betty is 5 more than 3 times Jadyn's age. Since Jadyn's age is unknown, we'll call that unknown variable x.

Betty is 5 more than 3 times x. Betty is also 41 years old.

Equation: 41 = 3x + 5

Now we have to solve for x

Solve for x:

41 = 3x + 536 = 3xx = 12

Jadyn is 12 years old.

Which of these could be the lengths of right triangle abc
A) 4,3,7
B) 5,7,12
C) 6,8,10
D) 7,8,15

Answers

Answer: C

Step-by-step explanation:

This is a Pythagorean triple.

what is the formula of equilateral triangle .class-8

Answers

Answer:

Step-by-step explanation:

The perimeter of an equilateral triangle is:

P = 3a (where a any length of the triangle)

The area of an equilateral triangle is:

[tex]A = \frac{\sqrt{3} }{4} a^{2}[/tex] (where a is the side length)

Using the area formula we can rearrange it to get the formula of the length of the equilateral triangle:

[tex]a = \frac{2}{3} 3^{\frac{3}{4} } \sqrt{A}[/tex]

If side is s

Then three important formulas are

[tex]\\ \rm\Rrightarrow Perimeter=3s[/tex](As sides are equal)

[tex]\\ \rm\Rrightarrow Area=\dfrac{\sqrt{3}}{4}s^2[/tex]

[tex]\\ \rm\Rrightarrow Height=\dfrac{\sqrt{3}s}{2}[/tex]

Pls help and explain it

Answers

Answer:

→ Compare the 2 grade A's

School B's is higher

→ Compare the 2 grade B's

School B's is higher

→ Now formulate a brief response

School B has more entrants in the exam and therefore has a higher proportion of students achieving top grades

Write the equation of the line tangent to
y = x^3 – 2x + 3 at x = -1.

Answers

Answer: y = x + 5

Step-by-step explanation:

Devaughn is 6 years older than Sydney. The sum of their ages is 80. What is Sydney's age?

Answers

Answer:

37 and 43

Step-by-step explanation:

There are some ways to do this, but this is what I like to do. First, since there are 2 people, I divide 80 by 2, which is 40. Now I add 3 to one person and subtract 3 from one person, because the age difference is 6 years, and there are two people (if you divide them you get 3). Now you get the answer; 37 and 43.

what is equivalent to 8x-12y+32

Answers

Answer:

C. 16(0.5x - 0.75y + 2) = 8x - 12y + 32

Step-by-step explanation:

Answer:

Yeah I got the answer

Step-by-step explanation:

C option is correct

We will have to take common like this

. 16(0.5x - 0.75y + 2) = 8x - 12y + 32

PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE

If each vowel in the word COLLEGE substitutes with the next letter of the English alphabetical series and each constant is substituted with the 2nd letter preceding it. How many vowels are present in the new arrangement? Fast plsssssssssssss with steps....

Answers

Answer:

Step-by-step explanation:

Following the substitution rules:

O becomes P and

E becomes F

because they are vowels(a,e,i,o,u) change to next letter.

C becomes A

L becomes J

G becomes E

because constants change to the letter two before the given letter.

So COLLEGE becomes APJJFEF

so it now has 2 vowels.

The dimensions of a rectangular garden were 5 m by 12 m. Each dimension was increased by the same amount. The garden then had an area of 120 m2. Find the dimensions of the new garden.

Answers

if dimensions were 5 and 12, that means ratio was 5:12. if we increase wach dimension by the same amount, the ratio is the same.

so:

5x×12x=120

60x²=120

x²=120÷60

x²=2

x=√2

that means each dimension was increased by √2

so dimensions are: 5√2 and 12√2

A bowl contains 7 white pebbles and 11 black pebbles. A pebble is chosen and not replaced, then another pebble is picked. What is the
probability that the first one is a white pebble and the second one a black pebble?
O a
7
18
Ob
11
18
Ос
11
17
Od
77
306

Answers

Answer:

17 because 2 is taken from 18 and 18-2=16 but 17 and 17 is close to 16

The figure formed by (−3, 2), (−4, 1), and (−1, −5) is translated 3 units right and 5 units up. What are the coordinates of the new figure?

Answers

Translating the figure involves chaging the position of the figure

The coordinates of the new figure are (0, 7), (1 , 6), and (2, 0)

The coordinates of the new figure

The coordinates are given as:

(−3, 2), (−4, 1), and (−1, −5)

The rule of translation 3 units right and 5 units up is:

(x + 3, y + 5)

So, we have:

(−3 + 3, 2 + 5), (−4 + 5 , 1 + 5), and (−1 + 3, −5 + 5)

Evaluate the sum

(0, 7), (1 , 6), and (2, 0)

Hence, the coordinates of the new figure are (0, 7), (1 , 6), and (2, 0)