SOLUTION: Find the number of distinguishable permutations of the group of letters: A,A,G,E,E,E,M.

Question 117046: Find the number of distinguishable permutations of the group of letters: A,A,G,E,E,E,M.
Found 2 solutions by edjones, MathLover1:
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
7!/2!*3! In the denominator the letters that appear more than once are factorialized.
=7*6*5*4*3*2/3*2*2
=7*5*4*3 the 6 is canceled by 3*2 and 2 is canceled by 2.
=420
Ed
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

Find the number of distinguishable permutations of the group of letters: ,,,,,,.
Here are the frequencies of the letters: , , , for a total of letters.

Then the number of distinguishable permutations will be:

�� do some simplification

so, the number of distinguishable permutations of the group of letters is .

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