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    Working with permutations and combinations

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    A concert to raise money for an economics prize is to consist of 5 works: 2 overtures, 2 sonatas, and a piano concerto.

    a) In how many ways can the program be arranged?

    b) In how many ways can the program be arranged if an overture must come first?

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    Solution Preview

    a) The factorial rule is used when you want to find the number of arrangements for ALL objects. You can calculate the number of possible ways to organize the program as follows.

    For the first concert, you have 5 different ...

    Solution Summary

    The permutations and combinations economic prizes are examined. How many ways the program can be arranged if an overture must come first are given.