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math - combinations

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To study the unity of Canada, a seven=person committee is to be selected from five public figures from Western Canada, five public figures from Central Canada, and five public figures from Eastern Canada.

I figured out parts a & b to this question, but I'm having troubles with c.

How many committees would have at least one representative from each region of Canada?

  • math - combinations -

    suppose nobody from WC is chosen
    no of ways to choose the committee is (10,6) or 210
    The same would be true for each of the other two regions.
    BTW, there is no way that 2 regions can be excluded, since we need 7 people and there would be only 5 available.

    So what we don't want is 3(210) or 630 , where one of the regions in excluded.

    without restrictions, no of committee's is (15,7) = 6435

    So number of committees with at least one person from each region is 6435 - 630 = 5805

  • math - combinations -

    i checked the answer key
    and it says 6075

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