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Word Problems/Permutation problem

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Question
Hi maam, can u pls help me with this problem.

6 boys and 6 girls are to be sitted in a row of 11 chairs such that the boys shall occupy only the odd numbers, find the number of all possible ways.

Tnx in adv! Just wanna know how to answer this.

Answer
Suppose there are n boys, and you need to seat r of them. There is no repetition (i.e., a boy cannot occupy more than one seat), but the order of seating matters. The number of arrangements is n!/(n-r)!.

In this case, n=6 and r=6.
6!/(6-6)! = 6!/0! = 6!/1 = 720
There are 720 ways to seat the boys in the odd chairs.

Similarly, there are 720 ways to seat the girls in the even chairs.

This gives a total of 720720 = 518,400 arrangements in which boys occupy only the odd chairs.

More information:
http://www.mathsisfun.com/combinatorics/combinations-permutations.html
Jump down to case #2, permutations without repetition.

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Janet Yang

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Word problems are my favorite type of math questions! I would not feel comfortable answering questions that require specialized knowledge (Physics, Statistics, etc.) because I have not studied these in depth.

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I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

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Co-author of An Outline of Scientific Writing: For Researchers With English as a Foreign Language.

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I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley, and a Master of Business Administration degree from The Wharton School.

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George White Elementary School. Homework Help program at the Ridgewood Public Library, Ridgewood, NJ. Individual students.

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