Question

How many numbers are there between 100 and 1000 such that every digit is either 2 or 9?

Answer 1

Clearly, the numbers between 100 and 1000 are 3-digit numbers.

So, we have to form 3-digit numbers by using 2 and 9.

Clearly, the repetition of digits is allowed.

Each one of the unit's, ten's and hundred's places can be filled in 2 ways.

Hence, the required number of numbers = $(2\times 2\times 2)=8.$