finite math

A tray contains 14 chocolate chip cookies and 16 oatmeal raisin cookies. How many ways can a child select 4 cookies that include at least 1 chocolate chip cookie?

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  1. Chocolate cookie -- C
    Oatmeal cookie ----O

    If the chocolate cookies are the same and the oatmeal cookies are the same ...
    there are only the following selections
    COOO
    CCOO
    CCCO
    CCCC

    If the cookies are different:
    1C,3O --- C(14,1)xC(16,3) = 7840
    2C,2O --- C(14,2)xC(16,2) = 10920
    3C,1O --- C(13,3)xC(16,1) = 4576
    4C ------C(13,4)xC(16,0) = 715
    for a total of 24051

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  2. 54

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