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Math Help - Help Please .... Permutations And Combinations

  1. #1
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    Exclamation Help Please .... Permutations And Combinations

    What is the number of sequences with the length m+k which is constructed from k appearances of 0 and m appearances of 1?

    here i think i know the answer :
    (m+k)!/m!.k!

    The second question is:
    In how much sequences from the question above there is no adjacent appearances of 1. That is no appearances of 11?

    find how many sets X that implies : |X| = 5 , X SUBSETS OR EQUALL to {1,2,3,...,14} and in X there exists no numbers that the difference between them is 1. In other words for every i, if i belongs to X, then i+1 doesn't belong to X

    PLEASE GUYS CAN YOU HELP ME . I REALLY NEED IT
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  2. #2
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    Quote Originally Posted by KOXKOXKOX View Post
    What is the number of sequences with the length m+k which is constructed from k appearances of 0 and m appearances of 1?
    here i think i know the answer :
    (m+k)!/m!.k!

    [COLOR=black]The second question is:
    In how much sequences from the question above there is no adjacent appearances of 1. That is no appearances of 11?

    find how many sets X that implies : |X| = 5 , X SUBSETS OR EQUALL to {1,2,3,...,14} and in X there exists no numbers that the difference between them is 1. In other words for every i, if i belongs to X, then i+1 doesn't belong to X
    Your first answer is correct.

    For the second we must have m \le k + 1 then the zeros form separators, like “_0_0_0_”, three zeros make four placesfor the 1's.
    So the answer is \binom{k+1}{m}.

    The third answer is the same as: “How many strings of nine zeros and five ones are possible if no two ones are consecutive?”
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