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Math Help - [SOLVED] counting problem - programs for radio station

  1. #1
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    Red face [SOLVED] counting problem - programs for radio station

    Can someone tell me if my solution is correct? There is a different answer in the book.
    Thanks!
    **********

    Beethoven wrote 9 symphonies, and Mozart 27 piano concerts.

    A station manager decides that on each successive night (7 days per week), a Beethoven symphony will be played, followed by a Mozart piano concerto, followed by a Schubert string quartet (of which there are 15). For roughly how many years could this policy be continued before exactly the same program would have to be repeated?

    MY SOLUTION
    B=9, M=27, Q=27
    Using the Multiplication Priniciple
    BxMxQ = 9x27x15 = 3645 3-day sequences,
    i.e. 3645 sets consisting of 3 days each.

    3645 sets x 3 days each set = 10935 days

    10935 / 365 days in a year = 29.95 years or approximately 30 years of non-repeating 3 day sequences.
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  2. #2
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    Why a three day sequence ?
    Aren't the three pieces played on the same night ?
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  3. #3
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    You're right.

    Quote Originally Posted by BobP View Post
    Why a three day sequence ?
    Aren't the three pieces played on the same night ?
    You are right. So the answer is 3654 days. Thanks.
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