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# In a family with 3 children, the parents have agreed to bring the chil

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Math Expert
Joined: 02 Sep 2009
Posts: 60460
In a family with 3 children, the parents have agreed to bring the chil  [#permalink]

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04 Dec 2019, 01:08
00:00

Difficulty:

95% (hard)

Question Stats:

32% (02:02) correct 68% (01:35) wrong based on 47 sessions

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In a family with 3 children, the parents have agreed to bring the children to the pet store and allow each child to choose a pet. This pet store sells only dogs, cats, and monkeys. If each child chooses exactly one animal, and if more than one child can choose the same kind of animal, how many different arrangements of animals could the family leave with?

A. 6
B. 8
C. 9
D. 10
E. 12

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Joined: 16 Feb 2015
Posts: 252
Location: United States
Concentration: Finance, Operations
Re: In a family with 3 children, the parents have agreed to bring the chil  [#permalink]

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04 Dec 2019, 01:20
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Bunuel wrote:
In a family with 3 children, the parents have agreed to bring the children to the pet store and allow each child to choose a pet. This pet store sells only dogs, cats, and monkeys. If each child chooses exactly one animal, and if more than one child can choose the same kind of animal, how many different arrangements of animals could the family leave with?

A. 6
B. 8
C. 9
D. 10
E. 12

Are You Up For the Challenge: 700 Level Questions

Explanation:

Total Cases can be:
MMM + MMC + MMB + DDD + DDC + DDM + CCC + CCD + CCM + MCB

Total Possibilities of arrangements: 10

IMO-D

Please give kudos, if you find my explanation good enough
Yale Moderator
Joined: 05 May 2019
Posts: 159
GPA: 3
Re: In a family with 3 children, the parents have agreed to bring the chil  [#permalink]

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16 Dec 2019, 01:51
Not sure why this question doesn't allow permutation.
CCD is different from CDC or DCC.
chetan2u
Math Expert
Joined: 02 Aug 2009
Posts: 8341
Re: In a family with 3 children, the parents have agreed to bring the chil  [#permalink]

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16 Dec 2019, 03:36
sharathnair14 wrote:
Not sure why this question doesn't allow permutation.
CCD is different from CDC or DCC.
chetan2u

Hi,

Arrangements could be combination or permutation depending on the context..

If say we were looking for arrangements in which the children could pick the pets, we could go with permutations 3*3*3.
But here we are looking at the arrangements in which the family can leave with. When picked up, all 3 pets are just a group and that group is the arrangement, so combinations is what we are looking for.
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Joined: 05 May 2019
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GPA: 3
Re: In a family with 3 children, the parents have agreed to bring the chil  [#permalink]

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16 Dec 2019, 03:50
chetan2u wrote:
sharathnair14 wrote:
Not sure why this question doesn't allow permutation.
CCD is different from CDC or DCC.
chetan2u

Hi,

Arrangements could be combination or permutation depending on the context..

If say we were looking for arrangements in which the children could pick the pets, we could go with permutations 3*3*3.
But here we are looking at the arrangements in which the family can leave with. When picked up, all 3 pets are just a group and that group is the arrangement, so combinations is what we are looking for.

Quote:
If each child chooses exactly one animal, and if more than one child can choose the same kind of animal, how many different arrangements of animals could the family leave with?

Hey, chetan2u Thanks and I totally understand your reasoning.
But doesn't this question explicitly state "different arrangements"? That is what caused this doubt.
However, I think now that the difference would be understood when one reads "how many different arrangements of animals" together. Fine margins. Maybe this question could have been a lot more difficult if one of the choices was a permutation product.
Re: In a family with 3 children, the parents have agreed to bring the chil   [#permalink] 16 Dec 2019, 03:50
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