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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
avatar+94092 
+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
 #2
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+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.

Guest Nov 25, 2018
 #3
avatar+94092 
0

Thanks guest, your praise really pleases me   laugh

Melody  Nov 25, 2018

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