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

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Find the number of distinguishable permutations of the group of letters: A,A,G,E,E,E,M.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!

Find the number of distinguishable permutations of the group of letters: A,A,G,E,E,E,M.
Here are the frequencies of the letters: A=2, G=1, E=3, M=1 for a total of 7 letters.
n+=+7
Then the number of distinguishable permutations will be:
n%21%2F%28%28n1%21%29%28n2%21%29%28n3%21%29%28n4%21%29%29
7%21%2F%28%282%21%29%281%21%29%283%21%29%281%21%29%29

1%2A2%2A3%2A4%2A5%2A6%2A7%2F%28%281%2A2%29%281%29%281%2A2%2A3%29%281%29%29
1%2A2%2A3%2A4%2A5%2A6%2A7%2F%282%2A6%29%29……… do some simplification
1%2A3%2A4%2A5%2A7
420%29

so, the number of distinguishable permutations of the group of letters is 420.