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Math Help - Combinations/Permutations Card problems

  1. #1
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    Combinations/Permutations Card problems

    You have a standard deck of 52 cards. How many possibilities are there if your turn 6 cards over one by one in the order: an ace, a king, an Ace, a King, an Ace, and a King?

    I am trying to help my friend out with his homework but its been so long since I have messed with permutations, combinations, and probability that I am blanking on remembering how to do it. Any help would be greatly appreciate for us. Thanks.
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    Re: Combinations/Permutations Card problems

    Quote Originally Posted by Tokenfreak View Post
    You have a standard deck of 52 cards. How many possibilities are there if your turn 6 cards over one by one in the order: an ace, a king, an Ace, a King, an Ace, and a King?
    (4)(4)(3)(3)(2)(2)
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    Re: Combinations/Permutations Card problems

    Quote Originally Posted by Plato View Post
    (4)(4)(3)(3)(2)(2)
    Ok, well that makes sense now since I have use that one king and ace and can't use that one again so it is one less each time. Thanks for that, helped out a lot. We have a ton more of these too do but we just need help on these next two and we should be able to do the rest since they are similar.


    You have a standard deck of 52 cards. How many possibilities are there if your turn 6 cards over one by one in the order: an ace, a king, an Ace, a King, an Ace, and a King and each next king is the same suit as the ace before it?

    You have a standard deck of 52 cards. How many possibilities are there if your turn 6 cards over one by one in the order: an ace, a king, an Ace, a King, an Ace, and a King and at least one of the kings is NOT the same suit as the ace before it?
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    Re: Combinations/Permutations Card problems

    Quote Originally Posted by Tokenfreak View Post
    You have a standard deck of 52 cards. How many possibilities are there if your turn 6 cards over one by one in the order: an ace, a king, an Ace, a King, an Ace, and a King and each next king is the same suit as the ace before it?
    (4)(1)(3)(1)(2)(1)

    Quote Originally Posted by Tokenfreak View Post
    You have a standard deck of 52 cards. How many possibilities are there if your turn 6 cards over one by one in the order: an ace, a king, an Ace, a King, an Ace, and a King and at least one of the kings is NOT the same suit as the ace before it?
    (4)(4)(3)(3)(2)(2)-(4)(1)(3)(1)(2)(1)
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    Re: Combinations/Permutations Card problems

    Ok, thanks that help us out a lot. We have now successfully finished all the problems with your help except for one last one that is stumping us.

    You have a standard deck of 52 cards. You pick a card, look at it, and return it back to the deck. You pick a card 6 times, but you have a bad memory and the only thing you remember are the suits of the picked cards, not even the order. How many possibilities are there?
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    Re: Combinations/Permutations Card problems

    Quote Originally Posted by Tokenfreak View Post
    You have a standard deck of 52 cards. You pick a card, look at it, and return it back to the deck. You pick a card 6 times, but you have a bad memory and the only thing you remember are the suits of the picked cards, not even the order. How many possibilities are there?
    I don't understand what is asked.
    How many possibilities are there? For what?
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    Re: Combinations/Permutations Card problems

    Quote Originally Posted by Plato View Post
    I don't understand what is asked.
    How many possibilities are there? For what?
    How many possibilities are there that you pick a card 6 times, look at it, and return it back to the deck; but you only remember the suits of the picked cards and not even the order.

    Thats the best I can rephrase it lol as I don't really understand what I am looking for either.
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    Re: Combinations/Permutations Card problems

    Quote Originally Posted by Tokenfreak View Post
    How many possibilities are there that you pick a card 6 times, look at it, and return it back to the deck; but you only remember the suits of the picked cards and not even the order.
    Thats the best I can rephrase it lol as I don't really understand what I am looking for either.
    Well it seems to be asking for content with respect to suits. Like all spades; three clubs, two diamonds, and heart; or whatever.
    If that is correct then the answer is \binom{6+4-1}{6!}=\frac{9!}{(6!)(3!)}.
    That is count of multi-selections.
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    Re: Combinations/Permutations Card problems

    Thanks again.
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