Suppose you have 22 cookies to share with your friends, Cassie, Mehmet, Nihar, P
ID: 3146978 • Letter: S
Question
Suppose you have 22 cookies to share with your friends, Cassie, Mehmet, Nihar, Paul, Sam, and Victoria.
a. How many ways are there to distribute the cookies among these 6 people? You may assume that you do not break any cookies into pieces, and you may give some people 0 cookies.
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Mehmet, Nihar and Paul all did not cheat on their Discrete Structures homework, so you decide to give each of them at least 4 cookies.
b. Now how many ways are there to distribute these cookies, satisfying this requirement?
Explanation / Answer
a. There are 22 cookies and 6 people.
r identical objects can be distributed among n containers in
(n + r - 1) C (n - 1) ways.
=> The number ways of distributing 22 cookies among 6 people
= (6 + 22 - 1) C (6 - 1)
= 27 C 5 ways.
= 80730 ways.
b. After giving Mehmet, Nihar and Paul their minimum of 4 cookies each, we are left with 10 cookies to be distributed among 6 people.
These can be distributed in (6 + 10 - 1) C (6 - 1)
= 15 C 5
= 3003 ways.
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