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Math Help - Factorials in a word problem

  1. #1
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    Factorials in a word problem

    Here is the word problem:

    Martha invited 4 friends to go with her to the movies. There are 120 different ways in which they can sit together in a row. In how many of those ways is Martha sitting in the middle?

    I need help with setting up the problem.
    If you can help, I really appreciate it!
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  2. #2
    Super Member Failure's Avatar
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    Quote Originally Posted by alaskamath View Post
    Here is the word problem:

    Martha invited 4 friends to go with her to the movies. There are 120 different ways in which they can sit together in a row.
    Because n objects can be arranged in a row in n!=1\cdot 2\cdot 3\cdots n ways.

    In how many of those ways is Martha sitting in the middle?

    I need help with setting up the problem.
    If you can help, I really appreciate it!
    Just imagine yourself placing these 5 people on 5 the seats of a row: You first place Martha in the middle (no alternative choice is possible here). The only choice that you have is how to arrange the 4 friends on the remaining 4 seats. And in how many ways can that be done? (Note that it doesn't matter whether the 4 remaining seats are next to each other or not.)
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  3. #3
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by alaskamath View Post
    Here is the word problem:

    Martha invited 4 friends to go with her to the movies. There are 120 different ways in which they can sit together in a row. In how many of those ways is Martha sitting in the middle?

    I need help with setting up the problem.
    If you can help, I really appreciate it!
    _ _ Martha _ _

    The first seat can be filled in 4 ways, the second seat in 3 ways, the third seat in only one way (Martha), the fourth seat in 2 ways and the fifth seat in one way.

    There are 4x3x1x2x1=24 ways.

    So, Martha is sitting in the middle in 24 of those ways.
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