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January 13th, 2016, 04:19 AM   #1
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Combination containing a pair

I've just been looking and permutations and combinations in a B&C textbook and one of the following exercises stumped me.

Q. There's several of each of nine items. How many combinations are there that contain 2 of the same item and two other different items.

The permutations for all different items is 9C4 = 9!/(5!4!) = 126 and all 4 the same would be 9.

The answer given for the Q is 252 and I can't see how they get this.

My solution would be that initially you have 9 choices then the second of the same item is a given and then what's left is the number of combinations of 2 from 7.

Soln: 9 * 1 * (7!/(5!/2!)) = 189 (ie. not the answer given 252).

What have I missed?
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January 13th, 2016, 06:20 PM   #2
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Wrong forum - try statistics
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January 28th, 2016, 12:08 PM   #3
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But certainly, just saying "There's several of each of nine items" is not enough. How many of the individual items? That will affect the answer.
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January 28th, 2016, 09:02 PM   #4
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I remember seeing the same problem in another forum with the same mistake. To get 252 use $\displaystyle 9\frac{8!}{6!2!}$
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