For those of you who know combinatorics, can you solve this problem?

Mariah recently gave a combinatorics problem that she was working on, and it reminded me of this problem. The twist needed to solve it is not usually taught in an intro class, but you should be able to figure it out.

I am sure you have all seen the type of test problem where you are given two columns of entries and you are asked to match the entries in the first column with those in the second. Suppose that you are given 6 rock bands in one column and the names of 6 songs in the second. Each band corresponds to one song. If you chose at random, what are the chances of getting at least 3 correct? You can’t use a band or song more than once.