How many positive integers less than 1000 can be written using the digits 2, 4, 5, and 6?

Question

How do you get the answer?

Answer 1

Assuming the digits can be repeated, and the numbers have no more than three digits, but can have 1, 2 or 3 digits, we start with single digits: there are 4 because we only have four to choose from: 2, 4, 5, 6. 2-digit numbers: there are 16 of these: 22, 24, 25, 26, 42, 44, ... There's a choice of four digits for the tens and the units, it's 4*4=16. For 3-digit numbers the choice of four digits applies to the hundreds, so there are 4*4*4=64 3-digit numbers. In total, then, we have 4+16+64=84.