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### Combinations and Permutations

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Date: 6/11/96 at 17:35:10
From: Anonymous
Subject: Permutations and combinations

There are 6 boys and four girls.  The boys do not have to stand
together, but they must be in order from shortest to tallest.
Of these ten people, how many ways can they line up together?

I have tried everything and I can not get the answer.
question because none of it is making sense to me.

Kristin
```

```
Date: 6/11/96 at 19:2:22
From: Doctor Anthony
Subject: Re: Permutations and combinations

I assume from the way you have worded the question that the girls can
be in any order amongst themselves, but the boys must be in the order
from shortest to tallest.

First we select 6 positions for the boys to occupy.  These positions
could be chosen in 10_C_6 ways = 210 ways.

This leaves 4 positions for the girls, and the girls can be rearranged
amongst themselves in 4! ways = 24 ways.  The boys, of course, can be
in only one order amongst themselves, so the overall number of ways
they could line up is given by 210*24 = 5040 ways.

I hope the explanation has been clear.  Write in again if you want
further help.

-Doctor Anthony,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Permutations and Combinations

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