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    kari1981's Avatar
    kari1981 Posts: 1, Reputation: 1
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    #1

    Mar 31, 2009, 07:50 AM
    Combinatorics in Choosing a Committee
    The student council wants to form a committee of 3 people to order pizzas for their next meeting. There are 20 members on the student council, 7 of which are vegetarians.

    How many different pizza committees can be formed if there must be at least 1 vegetarian and 1 non-vegetarian on the committee?
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #2

    Mar 31, 2009, 09:25 AM
    I assume that means at least one vegetarian and at least one non-vegetarian?

    Suppose we choose 1 vegetarian, then the other two must be non-vegetarian.

    C(7,1)C(13,2)=546

    2 vegetarians and 1 non-vegetarian:

    C(7,2)C(13,1)=273

    Add them up.
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