Question

How many 3 digit counting numbers less than 800 have digits that are all even?

Answer 1

75

Explanation:

Considering the possible values of each digit in turn:

First digit `{2, 4, 6}` Since the number `< 800` (Assuming a leading 0 is not allowed) = 3 possibles

Second digit `{0, 2, 4, 6, 8}` = 5 possibles

Third digit `{0, 2, 4, 6, 8}` = 5 possibles

Hence the number of 3 digit numbers `in NN < 800` where all digits are even is:

`3xx5xx5= 75`