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# Pat is to select six cookies from a tray containing only chocolate chi

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Math Expert
Joined: 02 Sep 2009
Posts: 59725
Pat is to select six cookies from a tray containing only chocolate chi  [#permalink]

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19 Mar 2019, 21:37
00:00

Difficulty:

65% (hard)

Question Stats:

48% (02:28) correct 52% (02:46) wrong based on 21 sessions

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Pat is to select six cookies from a tray containing only chocolate chip, oatmeal, and peanut butter cookies. There are at least six of each of these three kinds of cookies on the tray. How many different assortments of six cookies can be selected?

(A) 22
(B) 25
(C) 27
(D) 28
(E) 729

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Pat is to select six cookies from a tray containing only chocolate chi  [#permalink]

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Updated on: 20 Mar 2019, 23:55
Bunuel wrote:
Pat is to select six cookies from a tray containing only chocolate chip, oatmeal, and peanut butter cookies. There are at least six of each of these three kinds of cookies on the tray. How many different assortments of six cookies can be selected?

(A) 22
(B) 25
(C) 27
(D) 28
(E) 729

If the number of cookies of each of three types in assortment are a, b and c

Then we have an equation, a+b+c = 6

Now we have to find out whole number solutions of this equation.

Whole number solution = (n+r-1)C(r-1)

I.e. (6+3-1)C(3-1) = 8C2 = 28

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Originally posted by GMATinsight on 19 Mar 2019, 22:46.
Last edited by GMATinsight on 20 Mar 2019, 23:55, edited 1 time in total.
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Pat is to select six cookies from a tray containing only chocolate chi  [#permalink]

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Updated on: 20 Mar 2019, 23:36
2
Bunuel wrote:
Pat is to select six cookies from a tray containing only chocolate chip, oatmeal, and peanut butter cookies. There are at least six of each of these three kinds of cookies on the tray. How many different assortments of six cookies can be selected?

(A) 22
(B) 25
(C) 27
(D) 28
(E) 729

total cookies available of each type >=6
and total of each type available is >=6
so no of ways Pat can select
A. 0 chocolate cookies ; (0,6,0); (0,5,1); (0,4,2); (0,3,3); (0,2,4); (0,1,5); (0,0,6) total 7 ways
B. 1 chocolate cookies ;(1,5,0); (1,4,1); (1,3,2); (1,2,3); (1,1,4); (1,0,5) 6 ways
similarly we see until 2,3,4,5,6, chocolate cookies are chosen by Pat so total no of ways
7+6+5+4+3+2+1 = 28 assortments possible..
IMO D

Originally posted by Archit3110 on 20 Mar 2019, 00:33.
Last edited by Archit3110 on 20 Mar 2019, 23:36, edited 2 times in total.
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Joined: 14 May 2017
Posts: 3
Re: Pat is to select six cookies from a tray containing only chocolate chi  [#permalink]

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20 Mar 2019, 01:35
Wondering if there is a quicker method than counting..

I guess the answer is 27. Assuming each cookies of the same kind idential. And not count picking all 6 of the same kind e.g. 6 Choco or 6 Oatmeal

C O P
5 1 0
5 0 1
..5
..5
....5
....5
So,2*3=6

4 2 0
4 0 2
4 1 1
...
So, 3*3=9

3 3 0
3 0 3
3 2 1
3 1 2
...
So, 4*3=12

Total=6+9+12=27

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Re: Pat is to select six cookies from a tray containing only chocolate chi  [#permalink]

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20 Mar 2019, 23:35
GMATinsight wrote:
Bunuel wrote:
Pat is to select six cookies from a tray containing only chocolate chip, oatmeal, and peanut butter cookies. There are at least six of each of these three kinds of cookies on the tray. How many different assortments of six cookies can be selected?

(A) 22
(B) 25
(C) 27
(D) 28
(E) 729

The first cookie can be chosen in 3 ways (chocolate chip, oatmeal, or peanut butter)
The Second cookie can be chosen in 3 ways (chocolate chip, oatmeal, or peanut butter)
The Third cookie can be chosen in 3 ways (chocolate chip, oatmeal, or peanut butter)
.... and so on

Total ways of choosing 6 cookies = 3*3*3*3*3*3 = 729

GMATinsight
Sir the calculation which you have done will give total ways in which assortment 3 cookies can be chosen 6 times , whereas the question has asked for different assortments which can be made by choosing 6 different cookies..
Re: Pat is to select six cookies from a tray containing only chocolate chi   [#permalink] 20 Mar 2019, 23:35
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# Pat is to select six cookies from a tray containing only chocolate chi

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