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Math Help - Permutations and Combinations Problem!! Help!

  1. #1
    atlanticgal
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    Red face Permutations and Combinations Problem!! Help!

    television programmer to assign commercial slots to a 30 min program subject to following rules:

    -each commercial is one min long.
    -there are no consecutive commercial slots
    -the first min is not a commercial
    -the 2nd minute is a commercial
    -the last minute is a commercial
    -there must be at least two minutes of non commercials between commercial slots.

    a) if there are seven minutes of commercials in all, how many ways can the programer arrange them?

    ncnn-------------------------c

    pattern looks like this!

    b) what if the network decides to have 8 commercial minutes (follow same restrictions)?
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  2. #2
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    Quote Originally Posted by atlanticgal View Post
    -each commercial is one min long.
    -there are no consecutive commercial slots
    -the first min is not a commercial
    -the 2nd minute is a commercial
    -the last minute is a commercial
    -there must be at least two minutes of non commercials between commercial slots.
    a) if there are seven minutes of commercials in all, how many ways can the programer arrange them?
    ncnn-------------------------c
    In the above pattern you have accounted for five minutes and two commercials.
    There are these groupings left: cnn, cnn, cnn, cnn, cnn, n,n,n,n,n....
    That is: five blocks of cnn and ten individual ns.
    How many ways can those fifteen items be arranged?
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