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Math Help - Combinations

  1. #1
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    Combinations

    A cookie jar contains three chocolate-chip, two peanut-butter, one lemon, one almond, and five raisin cookies.?

    In how many ways can you select some cookies, if you must include at least one chocolate-chip cookie?

    the answer is 216, but i don't understand why it's 216 and not 215.. because i keep getting 215.

    Here's my reasoning:
    It's 215 because
    3 x 3 x 2 x2 6=216 BUT.. You CANNOT choose ZERO cookies, since you have to choose at least one chocolate chip cookie. Hence, choosing zero is not an option.. Now.. Subtract 1 from 216 = 215.

    What's wrong with my reasoning?
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  2. #2
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    Your calculation seems right. You don't have to subtract 1 because the "zero cookie" case actually contains 1 chocolate chip cookie.
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  3. #3
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    Hello, john-1!

    A cookie jar contains 3 chocolate-chip, 2 peanut-butter, 1 lemon, 1 almond, and 5 raisin cookies.

    In how many ways can you select some cookies,
    if you must include at least one chocolate-chip cookie?


    Here's my reasoning:
    It's 215 because: 3 x 3 x 2 x 2 x 6 = 216

    BUT.. You CANNOT choose ZERO cookies, since you have to choose at least one chocolate chip cookie.
    Hence, choosing zero is not an option.. Now.. Subtract 1 from 216 = 215.

    What's wrong with my reasoning?
    You have already considered the zero-cookie option in your counting.


    There are 3 chocolate chip cookies (C).
    And you said there are three choices:
    . . choose 1 C
    . . choose 2 Cs
    . . choose 3 Cs

    See?
    You've already eliminated the zero-C option.


    For the other cookies, you included the zero-cookie choice.

    There are two peanut buttter cookies (P).
    And you said there are three choices.
    . . choose 0 P
    . . choose 1 P
    . . choose 2 Ps


    Got it?

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