On the refrigerator, MATHEMATICS is spelled out with $11$ magnets, one letter per magnet. Two vowels and four consonants fall off and are put away in a bag. If the T's, M's, and A's are indistinguishable, how many distinct possible collections of letters could be put in the bag?
Let's find the total number of ways in which we can pick 2 vowels and 4 consonants from the 11 letters. Therefore the total number of possibilities is $4*(1+2*\binom{4}{2}+\binom{5}{4})=4*(1+12+5)=4*18=72$ Right, so there are 72 possibilities.

