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Math Help - Combinations

  1. #1
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    Combinations

    I have a question. The question is:

    You are buying 5 postcards from a shop that has 4 different postcards.

    1) In how many combinations can you buy 5 cards?
    2) How many possible combinations do 2 of the 4 different cards contain?

    My answers:

    1) \left(^{5}\mathcal{C}_4\right)=\frac{5!}{(4!)(5-4)!}= 5

    2) \left(^{4}\mathcal{C}_2\right)=\frac{4!}{(2!)(4-2)!}= 6

    Did I do it right or?

    Note: These are without repetitions only.
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  2. #2
    Senior Member TheAbstractionist's Avatar
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    I am assuming you made a slight typo in stating the question.

    Quote Originally Posted by Keep View Post
    You are buying 4 postcards from a shop that has 5 different postcards.

    1) In how many combinations can you buy 4 cards?
    Assuming that you buy 4 different postcards, your answers are correct.

    However, if you really are buying 5 postcards from a shop selling 4 postcards, then it is impossible for the 5 cards to be all different. In this case, assuming that there is no restriction on the number of cards that are the same, the answer is 4^5.
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  3. #3
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    Quote Originally Posted by TheAbstractionist View Post
    I am assuming you made a slight typo in stating the question.


    Assuming that you buy 4 different postcards, your answers are correct.
    Sorry, it is not a typo. That is how the question is. There are 4 different types of postcards in stock in the shop. And you want to buy 5 cards.
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  4. #4
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    Quote Originally Posted by TheAbstractionist View Post

    However, if you really are buying 5 postcards from a shop selling 4 postcards, then it is impossible for the 5 cards to be all different. In this case, assuming that there is no restriction on the number of cards that are the same, the answer is 4^5.
    Yeah that is how the question is. You are buying 5 cards from a shop that has 4 different postcards. So I get the answer to 1). The answer to 2) is also 4^2 or?
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