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Pre Calculus 12

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an orchestra has 2 violinsts, 2 cellisst, and 4 harpists. Assume that the players of each instrument have to sit together, but they can sit in their own group. In how many ways can the conductor seat the members of the orchestra in a line?

I just went 4*3*2 and got 24? is that wrong?

  • Pre Calculus 12 -

    visualize the groups V,C,H
    these groups can be arranged in 3! ways or 6 ways

    but within each group, the
    violinists can be arranged in 2 way
    the cellists in 2 ways
    the harpists in 4! or 24 ways

    so the number of arrangements
    = 6(2x2x24) or 576 ways

  • Pre Calculus 12 -

    Oh but this is a multiple choice question and the only answers that it can be are

    A 144
    B 72
    C 24
    D 1728

  • Pre Calculus 12 -

    It looks to me like you have a typo somewhere. Your answer of 4*3*2 indicates that there were 3 violinists or 3 harpists. In that case, multiply Reiny's answer by 3 to get 1728.

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