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# a) Emma has 8 chocolate chip cookies and 7 gingerbread cookies. In how many ways can she distribute these cookies to four of her friends?

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a) Emma has 8 chocolate chip cookies and 7 gingerbread cookies. In how many ways can she distribute these cookies to four of her friends? (without breaking the cookies into pieces)

b) Jim has 6 cookies that he wants to distribute to 5 children. If all the cookies are identical, and two of the children are twins who insist on receiving an equal number of cookies, then how many ways can I distribute the cookies?

Feb 25, 2020

#1
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(a):

Focusing on the chocolate chip cookies, we notice that dividing 8 cookies into 4 groups is a classic stars/stripes problem. Distributing 8 cookies among 4 friends is C(11,3) ways.

In each of the above realities, you can also similarly divide 7 cookies into 4 groups to find C(10,3).

C(11,3)*C(10,3) = 165*120 = 19800.

(b):

Ways to distribute among 3 other children...

If twins get 0 cookies: C(8,2) = 28

1 cookie: C(6,2) = 15

2 cookies: C(4,2) = 6

3 cookies: I mean, the twins already have every cookie... (it's C(2,2) = 1)

Sum = 28 + 15 + 6 + 1 = 50 ways total.

Feb 25, 2020
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Thanks so much for explaining the problem to me!!!

mathmathj28  Feb 26, 2020