# Math Help - digits

1. ## digits

Of all the four-digit positive integers containing only digits from the set {2, 4, 6, 8}, what fraction of them have at least one of their digits repeated? Express your answer as a common fraction.

2. Originally Posted by sri340
Of all the four-digit positive integers containing only digits from the set {2, 4, 6, 8}, what fraction of them have at least one of their digits repeated? Express your answer as a common fraction.
Hi sri340,

We can ask "how many have no repeated digits" ?

This is 4! as all 4 digits must be different.

There are $4^4$ 4-digit numbers given the digits may be repeated.

Hence $4^4-4!$ contain at least one repeated digit.

The fraction is $\frac{4^4-4!}{4^4}=\frac{4(4^3-6)}{4(4^3)}=\frac{4^3-6}{4^3}$