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Math Help - Combinations Help

  1. #1
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    Combinations Help

    In how many ways can 12 prices be awarded evenly among four people?

    I am not sure how to start this question.

    Also, one more:

    From a deck of 52 cards, how many different four-card hands could be dealt which include one from each suit?

    Again, I do not know where to start. Additionally, if anyone can link me to a source with more of these combination questions (deck of card questions), that would be great.

    Many thanks,

    Needs Help
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  2. #2
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    Warning My responses to combinations questions are notoriously inaccurate

    How many ways can 12 prizes be awarded amongst 4 people.
    12!/3!

    You know that each person gets 3 prizes.
    There are 12! ways of distributing the prizes, and each person gets 3 of them. But the order of the 3 prizes receieved doesn't matter. there are 3! ways of ordering the set of 3 prizes receieved


    From a deck of 52, how many 4 card hands include 1 from each suit
    There are 4 suits in a standard deck of cards. So you must choose 1 of the 13 spades, then 1 of the 13 clubs,....etc

    There are 13*13*13*13 ways of doing that. However the order does not matter so the final answer is

    13*13*13*13 / 4!

    (there are 4! ways of ordering the 4 suits)
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  3. #3
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    Quote Originally Posted by SpringFan25 View Post
    Warning My responses to combinations questions are notoriously inaccurate

    How many ways can 12 prizes be awarded amongst 4 people.
    12!/3!

    You know that each person gets 3 prizes.
    There are 12! ways of distributing the prizes, and each person gets 3 of them. But the order of the 3 prizes receieved doesn't matter. there are 3! ways of ordering the set of 3 prizes receieved


    From a deck of 52, how many 4 card hands include 1 from each suit
    There are 4 suits in a standard deck of cards. So you must choose 1 of the 13 spades, then 1 of the 13 clubs,....etc

    There are 13*13*13*13 ways of doing that. However the order does not matter so the final answer is

    13*13*13*13 / 4!

    (there are 4! ways of ordering the 4 suits)
    Thanks for the help, however, these are inaccurate. Thanks, though.
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  4. #4
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    Quote Originally Posted by NeedsHelpp View Post
    In how many ways can 12 prices be awarded evenly among four people?

    I am not sure how to start this question.

    Also, one more:

    From a deck of 52 cards, how many different four-card hands could be dealt which include one from each suit?

    Again, I do not know where to start. Additionally, if anyone can link me to a source with more of these combination questions (deck of card questions), that would be great.

    Many thanks,

    Needs Help
    12 prizes can be divided evenly among 4 people in

    12! / (3!)^4

    ways. One way to look at this is as a "multinomial coefficient". Another way is that the prizes can be ordered in 12! ways with person #1 getting 1-3, #2 getting 4-6, etc., but the ordering of gifts for each person doesn't matter.

    For the card problem, there are 13 ways to pick a club, 13 ways to pick a spade, etc., so there are 13^4 possible hands. (We don't need to divide by 4! because we specified the suites.)
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  5. #5
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    i think ill stop answering these ones
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