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You have $15$ marbles and three jars labeled A, B, and C. How many ways can you put the marbles into the jars…

(a) If each marble is different? (My answer C(15,3) )

(b) If each marble is the same? ( My Answer that i think is C(15+3-1,3) as order doesnt matter) NOT SURE THOUGH!!

(c) If each marble is the same and each jar must have at least two marbles?

(d) If each marble is the same but each jar can have at most 6 marbles?

(e) If you have 10 identical red marbles and 5 identical blue marbles?

I am not sure about my answer so any help would be appreciated.

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    so would (a) be 3x15! ?2011-12-02
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    oh so it would 3^15 for (a) ?2011-12-02
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    and for (c) how would you go about starting it?2011-12-02
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    On (b), I didn't notice you had $\binom{15+3-1}{3}$, it should be $\binom{15+3-1}{3-1}$. For details see Stars and Bars on Wikipedia.2011-12-02
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    how would you start part c?2011-12-02
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    Your questions are not well stated and @André Nicolas answer assumes that the some of the jars may be left empty in an arrangement.2011-12-02

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