Combinations and PermutationsDate: 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/ |
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