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?

mathtoo Nov 24, 2018

#1**+3 **

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?

I just chose to count them

a a e i choose 2 and m m t t h c s choose 4

vowels first

aa

ae

ai

ei

thats it 4 ways to chose the vowels

now

m m t t h c s choose 4

I will use m and t for themselves and * for any other letter

mmtt (1)

mmt* (3)

mm** (3)

ttm* (3)

tt** (3)

mt** (3)

m*** (1)

t*** (1)

total = 18 ways

4*18=72

So there are 72 distinct combinations of 2 vowels and 4 consonants.

Melody Nov 25, 2018