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# George went to the supermarket with a red and a green bag

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Intern
Joined: 27 Aug 2015
Posts: 4
George went to the supermarket with a red and a green bag  [#permalink]

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09 Sep 2015, 00:33
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Difficulty:

55% (hard)

Question Stats:

60% (01:46) correct 40% (02:05) wrong based on 123 sessions

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George went to the supermarket with a red and a green bag and bought 10 carrots and 6 radishes. On the way back he divided the vegetables between the two bags in such a way that no bag was left empty. What is the maximum number of ways in which he can divide the vegetables between the two bags?

(A) 60
(B) 120
(C) 600
(D) 2^16
(E) 2^16 - 2

Senior Manager
Joined: 05 Apr 2015
Posts: 357
Re: George went to the supermarket with a red and a green bag  [#permalink]

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09 Sep 2015, 01:25
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2
Hi,

It is E.

Each carrot or radish can go into either red or green bag. So for Each vegetable there are 2 ways they can end up.

Like that for 16( 10 carrot + 6 raddish) there are 2^16 ways. But this includes the cases where all the 16 are in either red or green bag.

Regards,
Dom.
##### General Discussion
Manager
Joined: 12 Mar 2018
Posts: 106
George went to the supermarket with a red and a green bag  [#permalink]

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28 Nov 2018, 13:36
2
The info that carrots and radishes are not identical is considered as de-facto?
If the carrots and radishes are identical, then the answer would be [17! / (10!*6!)] - 2
Manager
Joined: 07 Jun 2017
Posts: 100
Re: George went to the supermarket with a red and a green bag  [#permalink]

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02 Aug 2017, 21:25
1
dominicraj wrote:
Hi,

It is E.

Each carrot or radish can go into either red or green bag. So for Each vegetable there are 2 ways they can end up.

Like that for 16( 10 carrot + 6 raddish) there are 2^16 ways. But this includes the cases where all the 16 are in either red or green bag.

Regards,
Dom.

Dear Dom,

I got the first part, but I don't get the second. Why do you -2 at the end?
Thank you so much
Manager
Joined: 17 Aug 2015
Posts: 96
Re: George went to the supermarket with a red and a green bag  [#permalink]

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13 May 2016, 22:36
himanksharma9590 wrote:
George went to the supermarket with a red and a green bag and bought 10 carrots and 6 radishes. On the way back he divided the vegetables between the two bags in such a way that no bag was left empty. What is the maximum number of ways in which he can divide the vegetables between the two bags?

(A) 60
(B) 120
(C) 600
(D) 2^16
(E) 2^16 - 2

I have a question. Do we need to assume that each carrot is not identical to the other carrot and a radish is not identical to another.
What if each of the carrots and each of the radish were identical within each group.
If that is the case then I am getting a different answer as opposed to the OA. Can someone help me please?
Intern
Joined: 24 Jan 2019
Posts: 4
Re: George went to the supermarket with a red and a green bag  [#permalink]

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30 Nov 2019, 16:59
pclawong wrote:
dominicraj wrote:
Hi,

It is E.

Each carrot or radish can go into either red or green bag. So for Each vegetable there are 2 ways they can end up.

Like that for 16( 10 carrot + 6 raddish) there are 2^16 ways. But this includes the cases where all the 16 are in either red or green bag.

Regards,
Dom.

Dear Dom,

I got the first part, but I don't get the second. Why do you -2 at the end?
Thank you so much

Hi pclawong. Better 2 years late than never!

The reason you subtract 2 at the end is because when you perform 2^16 to find the total possibilities, the outcome will include one possibility where the red bag contains every vegetable and one possibility where the green bag contains every vegetable. The question expressly prohibits this, so you subtract those two possibilities from 2^16.
Intern
Joined: 09 Oct 2019
Posts: 12
Location: Spain
Concentration: General Management, Finance
Schools: LBS, Said Oxford
GMAT 1: 700 Q46 V40
GPA: 3.85
Re: George went to the supermarket with a red and a green bag  [#permalink]

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13 Dec 2019, 15:10
faltan wrote:
The info that carrots and radishes are not identical is considered as de-facto?
If the carrots and radishes are identical, then the answer would be [17! / (10!*6!)] - 2

Can you explain the formula please?
Re: George went to the supermarket with a red and a green bag   [#permalink] 13 Dec 2019, 15:10
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