Question

Consider the following problem: A student brings 8 chocolate chip cookies, and 7 oatmeal raisin cookies, to his seminar of 5 students and 1 teacher. If all the cookies are eaten, how many distributions of the cookies to the class are there?

(a) (5 points) List some possible distributions of the chocolate chip cookies, and symbolize each of these using C's and L's

(b) (5 points) Use o’s and|’s to list an impossible distribution of the oatmeal raisin cookies.

(c) (5 points) How many distributions of the cookies are there? Show your work

Answer 1

ANSWER

Given that:

A student brings 8 chocolate chip cookies, and 7 oatmeal raisin cookies, to his seminar of 5 students and 1 teacher. If all the cookies are eaten, how many distributions of the cookies to the class are there?

a) List some possible distributions of the chocolate chip cookies, and symbolize each of these using
c’s and |’s.

We distribute 8 cookies into 6 persons.So here 5 partition denoted by '|' and cookies are denoted by c.Possible distribution are

c|cc|cc|cdc; cccccccc

cccccccc; ccccccccc and SO on

b) Use o’s and |’s to list an impossible distribution of the oatmeal raisin cookies.

Here we distribute 7 oatmeal raisin cookies (denoted by '0') into 6 person so on impossible distribution is given by

0

c) How many distributions of the cookies are there?

Here 6 persons (denoted by xi's) and 8 cookies (c) .We have 5 partitions ways to distribute 8c's

c2.cc .cs.cpe

cPicc|p2 cc|P3 P4 cc|P5 P3 P4 cc|P5 → 122120

pic CP2 CP3 cc|P4 cc|P5C |P4 cc PC +021121

cc CP CP2 C3 |P3 с |P4 CPS c +311111 and so on

Here total arrangements of distribution = of 8'c and 5 p's (cccccccc ppppp)

8! 8! 1287

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