How many integers are there between 100 and 1000 all of whose digits are even?

Q. How many integers are there between 100 and 1000 all of whose digits are even?

(A) 60

(B) 80

(C) 100

(D) 90

Ans: 100

We need the numbers between 100 and 1000 and all the digits should be even.

As the required numbers are greater than 100 and less than 1000, all the numbers have 3 digits only.

As we can fill each digit with an even number,

Possible even numbers to fill unit place = 0, 2, 4, 6, 8 (5 possibilities)

Possible even numbers to fill tens place = 0, 2, 4, 6, 8 (5 possibilities)

Possible even numbers to fill hundreds place = 2, 4, 6, 8 (4 possibilities)

Total number of choices =