+0

# Combinations

+2
979
3
+816

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?

Nov 24, 2018

#1
+109524
+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.

Nov 25, 2018
#2
+1

Congrats Melody!! This question is on the Internet and the "Best" answer is about a page long by some guy, which eventually arrives at the same answer of 72!!!. Your method is so simple and intuitive that, almost, anybody can understand it.

Nov 25, 2018
#3
+109524
0