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?
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.