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Finite Math

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The reading list for a literature class has 6 fiction and 8 nonfiction books. A student is to write a report on 5 books from the list during the semester. The report must include at least 1 and at most 4 reports of fiction books. In how many ways can the selection of books be made?

  • Finite Math -

    number of ways without restriction = C(14,5) = 2002

    What we CAN'T have is no fiction or all 5 fiction

    number of ways no fiction = (6,0)xC(8,5) = 56
    number of ways all fiction - C(6,5)xC(8,0) = 6

    no of ways of your event = 2002 - 56 - 6 = 1940

    The longer way would be to find
    1F, 4NF = C(6,1) x C(8,4) = 420
    2F , 3NF = C(6,2) x C(8,3) = 840
    3F , 2NF = C(6,3) x C(8,2) = 560
    4F, 1NF = C(6,4) x C(8,1) = 120
    total = 1940

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