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# 6 children ,9 chairs ,how many arrangements?

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6 children ,9 chairs ,how many arrangements? [#permalink]  18 Sep 2013, 04:57
6 children ,9 chairs ,how many arrangements?

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Re: 6 children ,9 chairs ,how many arrangements? [#permalink]  18 Sep 2013, 18:36
Expert's post
aman kumar wrote:
6 children ,9 chairs ,how many arrangements?

Hi aman,

for a problem like this, it's typically best to break it up into pieces. We have two questions. First, how many ways are there to chose six chairs out of nine to seat children in? And second, how many ways are there to arrange the six children in the chairs we've chosen?

Once we've broken the question down into it's component parts, it's a simple matter of applying formulas. The first choice is an unordered combination, and the second is a simple ordering of a group. So:

[9!/(3!6!)] * 6! = [9!/(3!6!)] * 6! = 60,480

(Note: from a purely mathematical perspective, this problem is the same as 9P6, which is simpler math. If you can figure out why, great! But the reason that works isn't immediately obvious, and the solution above isn't very much longer.)
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Re: 6 children ,9 chairs ,how many arrangements?   [#permalink] 18 Sep 2013, 18:36
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# 6 children ,9 chairs ,how many arrangements?

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