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Math Help - Combinations/Permutations

  1. #1
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    Talking Combinations/Permutations

    From "Discrete Mathematics with Graph Theory"
    by Goodaire and Parmenter

    Page 236 # 16

    There are 5 single rooms, 5 double rooms, and 5 triple rooms in a college. In how many ways can 30 students be assigned to the 15 rooms? (All rooms are numbered).

    Thanks!

    I'm thinking theres 15 spots (5 singles, 5 doubles, 5 triples) and 30 people go into those spots. But Then I'm confused from there.
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  2. #2
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    Re: Combinations/Permutations

    There are 30 spots because 5 are singles(5), 5 are doubles (10), and 5 are triples (15).
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  3. #3
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    )^5

    Hello, ThatPinkSock!

    There are 5 single rooms, 5 double rooms, and 5 triple rooms in a college.
    In how many ways can 30 students be assigned to the 15 rooms? .(All rooms are numbered).

    \text{Answer: }\:\frac{30!}{(1!)^5(2!)^5(3!)^5}
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