SOLUTION: How many distinguishable permutations are possible with all the letters of the word ELLIPSES?

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Question 1176491: How many distinguishable permutations are possible with all the letters of the word ELLIPSES?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
ELLIPSES has 8 letters, 2 Es, 2Ls, and 2+S, 1 I, and 1 P
The formula for indistinguishable permutation is
n!/(n[1]!n[2]!.....n[k]!)
where n is the total number of objects and are the number of indistinguishable objects.
We have 2Es, 2Ls, and 2S (1 I, and 1 P will not make any difference); the formula then becomes:
8%21%2F%282%212%212%21%29
=%288%2A7%2A6%2A5%2A4%2A3%2A2%29%2F%282%2A2%2A2%29
=
=8%2A7%2A3%2A5%2A2%2A3
=5040
There are 5040 distinguishable permutations of the word ELLIPSES.