## A woman has seven cookies - four chocolate chip and three oatmeal. She gives one cookie to each of her six children

##### This topic has expert replies
Moderator
Posts: 6689
Joined: 07 Sep 2017
Followed by:21 members

### A woman has seven cookies - four chocolate chip and three oatmeal. She gives one cookie to each of her six children

by BTGmoderatorDC » Sat Jul 02, 2022 8:53 pm

00:00

A

B

C

D

E

## Global Stats

A woman has seven cookies - four chocolate chip and three oatmeal. She gives one cookie to each of her six children: Nicole, Ronit, Kim, Deborah, Mark, and Terrance. If Deborah will only eat the kind of cookie that Kim eats, in how many different ways can the cookies be distributed?

(A) 5040
(B) 50
(C) 25
(D) 15
(E) 12

OA D

Source: Manhattan Prep

Master | Next Rank: 500 Posts
Posts: 409
Joined: 15 Oct 2009
Thanked: 27 times

### Re: A woman has seven cookies - four chocolate chip and three oatmeal. She gives one cookie to each of her six children

by regor60 » Sun Jul 10, 2022 6:39 am
Distributing 6 cookies can be done in the following ways:
3 chocolate, 3 oatmeal
4 chocolate, 2 oatmeal

Pairing Deborah and Kim (D and K) together, let's examine each way above:

D&K can each have a chocolate cookie, in which case there are 4 choices of children for the remaining chocolate cookie. The remaining children get oatmeal.
4 ways

Same logic holds if D&K get oatmeal cookies instead:
4 ways

Now let's examine the 4 chocolate/2 oatmeal scenario:

D&K get chocolate cookies. Two children can be selected from the remaining 4 to receive the other chocolate cookies as follows;
4!/2!2! = 6 ways. The other 2 children get oatmeal.

D&K get oatmeal cookies. The other children get chocolate. 1 way

Total ways 15,D

• Page 1 of 1