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jmc

counting and probability senior

Problem

On the refrigerator, MATHCOUNTS is spelled out with 10 magnets, one letter per magnet. Two vowels and three consonants fall off and are put away in a bag. If the Ts are indistinguishable, how many distinct possible collections of letters could be put in the bag?
Solution
Let's divide the problem into two cases: one where 0 or 1 T's fall off and one where both T's fall off:

0 or 1 T's:

2 T's:

Total:
Final answer
75