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

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

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New post 09 Sep 2015, 00:33
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  55% (hard)

Question Stats:

57% (01:47) correct 43% (02:05) wrong based on 102 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

Please explain in detail
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Re: George went to the supermarket with a red and a green bag  [#permalink]

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New post 09 Sep 2015, 01:25
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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.

So answer is 2^16-2.

Regards,
Dom.
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Re: George went to the supermarket with a red and a green bag  [#permalink]

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New post 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

Please explain in detail



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?
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Re: George went to the supermarket with a red and a green bag  [#permalink]

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New post 02 Aug 2017, 21:25
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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.

So answer is 2^16-2.

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

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New post 28 Nov 2018, 13:36
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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
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Re: George went to the supermarket with a red and a green bag  [#permalink]

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New post 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.

So answer is 2^16-2.

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.
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Re: George went to the supermarket with a red and a green bag   [#permalink] 30 Nov 2019, 16:59
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George went to the supermarket with a red and a green bag

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