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

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Bunuel
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Pat is to select six cookies from a tray containing only chocolate chi [#permalink] New post   19 Mar 2019, 21:37
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A
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95% (hard)

Question Stats:

45% (02:27) correct 55% (02:28) wrong based on 98 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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D
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GMATinsight
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Re: Pat is to select six cookies from a tray containing only chocolate chi [#permalink] New post   16 Jul 2020, 03:24
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rishit924 wrote:
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


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

Answer: Option D


Dear Sir,
Could you please enlighten on this method?
What is this whole number solution and from where equation (n+r-1)C(r-1) came from?

Thanks in advance


rishit924

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Pat is to select six cookies from a tray containing only chocolate chi [#permalink] New post   Updated on: 20 Mar 2019, 23:55
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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

Answer: Option D

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] New post   Updated on: 20 Mar 2019, 23:36
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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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Re: Pat is to select six cookies from a tray containing only chocolate chi [#permalink] New post   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] New post   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

Answer: Option E


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..
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Re: Pat is to select six cookies from a tray containing only chocolate chi [#permalink] New post   16 Jul 2020, 03:17
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


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

Answer: Option D


Dear Sir,
Could you please enlighten on this method?
What is this whole number solution and from where equation (n+r-1)C(r-1) came from?

Thanks in advance
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Re: Pat is to select six cookies from a tray containing only chocolate chi [#permalink] New post   17 Mar 2024, 05:33
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Re: Pat is to select six cookies from a tray containing only chocolate chi [#permalink]
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