We call a natural number "nice" if there are only even digits in its recording. How many "nice" four-digit numbers are there?

Answer:

I suppose that this refers to numbers like:

N = abcd

Where a, b, c and d are single digits.

We want to find the number of 4-digit numbers such that:

a, b, c and d are even numbers.

So let's count the number of options for each digit, where we impose that the possible digits must be even.

a: Here we have the options {2, 4, 6, 8} ( 0 is an even digit, but if we take a = 0, then this would be a 3 digit number) Then we have 4 options for a.

b: Here we have the options {0, 2, 4, 6, 8}. 5 options in total.

c: Here we have the options {0, 2, 4, 6, 8}. 5 options in total.

d: Here we have the options {0, 2, 4, 6, 8}. 5 options in total.

The total number of possible combinations will be equal to the product of the number of options for each selection.

C = 4*5*5*5 = 500

There are 500 "nice" numbers of 4-digits.

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