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Math Help - Combination

  1. #1
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    Combination

    If I have 9 varieties of pizza to choose from, in how many ways can I choose 4 slices of pizza ?
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  2. #2
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    Hello, fholik!

    If I have 9 varieties of pizza to choose from,
    in how many ways can I choose 4 slices of pizza?

    For each of the four slices, you have 9 choices of variety.

    Therefore, there are: . 9^4 \,=\,6561 ways.

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  3. #3
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    combination

    Thanks for the reply, but your method leaves duplicate choices. This question came from an state-sponsored math exam and the correct response is 495. I just need to find the formula for future reference.
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  4. #4
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    Quote Originally Posted by fholik View Post
    Thanks for the reply, but your method leaves duplicate choices. This question came from an state-sponsored math exam and the correct response is 495. I just need to find the formula for future reference.
    The question is vague. But the given answer implies a multi-set.
    The number of ways to put K identical units into N different cells is \binom{K+N-1}{K}.
    Here the choices are identical and the pizzas are different.
    \binom{4+9-1}{4}=495
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  5. #5
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    combination

    Thank You, Plato. That is the formula I was looking for. I had seen it a few months ago, but had forgotten. Thanks for reminding me. I will write it down this time. Fholik
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