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Basic Permutation Example

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Please help with the following combinatorics problems.

Sarah, Jolly and Betty are female triplets. They and their 10 cousins are posing for a series of photographs. One pose involves all 13 children. How many ways can the 7 boys and 6 girls be arranged in one row under each of the following conditions?

a) The boys and girls must alternate positions.
b) The triplets must stand next to each other.

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Solution Summary

This is a basic combinatorics problem demonstrating the concepts of factorials (!), permutations, and combinations. It is appropriate for introductory courses in probability and statistics. It provides an example problem involving basic permutations that includes arranging boys and girls in a photograph. Explanations an calculations are provided in the solution.

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a) The boys and girls must alternate positions.

The answer is 7! x 6!. If the boys and girls must alternate positions, then the row must begin with a boy, followed by a girl, etc. in something like the following: B G B G B G B G B G B G B. ...

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