Question

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?

Answer 1

Answer: 75 distinct possible collections

Explanation:

2 vowels = 3C2 = 3

3 vowels = 25 ways

25 * 3 = 75 total ways

Answer 2

630 distinct possible collections of letters could be put in the bag.

Explanation:

Since on the refrigerator, MATHCOUNTS is spelled out with 10 magnets, one letter per magnet, and two vowels and three consonants fall off and are put away in a bag, if the Ts are indistinguishable, to determine how many distinct possible collections of letters could be put in the bag, the following calculation must be performed:

Vowels: 3

(AO, AU, OU)

Consonants: 7

3 x 7 x 6 x 5 = X

3 x 210 = X

630 = X

Therefore, 630 distinct possible collections of letters could be put in the bag.