Combinations and Permutations

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.
Please help me!  I need you to start at the beginning of the 
question because none of it is making sense to me.

Thank you for your help,  
    
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.

Answer is 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/