How many possibilities can come out of this string "DDDDDOGGYYY?"

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Originally Posted by trey123

How many possibilities can come out of this string "DDDDDOGGYYY?"

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Two ways of solving this type of problem:

Method 1. Figure out how many words you would have if all the letters were different, then get rid of the repeats by dividing by the number of ways that the D's can be arranged, and the dividing by the number of ways the O's can be arranged etc.

Method 2. Given a total of N letters (in this case N = 11), then there are 11 positions to place the 5 D's. So the number of ways that the D's can be arranged is C(11,5). After the D's are placed there are 6 spots "open" - so the O can go into one of 6 places. After the O is placed that leaves 5 spots for 2 G's, so the G's an be placed in C(5,2) ways. And then finally that leaves just 3 places for the 3 Y's, so there's only one way to do that. Multuiply these possibilities and the answer should be the same as with method 1.

Let's try an example - suppose you have AAABBC. Method 1 gives 6!/(3! X 2! X 1!) = 120. Method 2 gives C(6,3) x C(3,2) x C(1,1) = 120.

Post back with what you get for an answer and we'll check it for you.

Is it, 11!/(5!*3!*2!*1!) = 27720?

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Originally Posted by trey123

Is it, 11!/(5!*3!*2!*1!) = 27720?

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Correct!

Thank you very much!