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# From a group of three boys and four girls, a school hallway monitor gr

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Math Expert
Joined: 02 Sep 2009
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From a group of three boys and four girls, a school hallway monitor gr  [#permalink]

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31 Jan 2017, 10:04
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Difficulty:

15% (low)

Question Stats:

76% (00:42) correct 24% (00:50) wrong based on 207 sessions

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From a group of three boys and four girls, a school hallway monitor group is to be selected. If the group is to be formed of one boy and four girls, how many different such groups can be formed?

A. 1
B. 3
C. 36
D. 72
E. 360

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Joined: 09 Oct 2016
Posts: 19
Schools: HBS '19
From a group of three boys and four girls, a school hallway monitor gr  [#permalink]

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31 Jan 2017, 16:18
Bunuel wrote:
From a group of three boys and four girls, a school hallway monitor group is to be selected. If the group is to be formed of one boy and four girls, how many different such groups can be formed?

A. 1
B. 3
C. 36
D. 72
E. 360

I don't want to be rude but I did not understand whether positions are considered unique or not, anyway I'll answer in both cases:

In case positions are identical:
we need to form a group of 5 people in which 4 of them has to be girls. we already have 4 girls so no arranging here (only 1 option for arranging). we do have 3 boys and only 1 spot for 1 boy, so 3 options for the boys - so we can form 3 groups (each group has different boy)

In case positions are unique:
let's start with the girls. let's assume that there are only 4 spots. the options for arranging the girls in those 4 spots are:
4! = 1*2*3*4 = 24
now, let's add the 5th spot. in every arrangement there will be 1 "Free" spot (not really free because one of the boys will sit there), so we can have 5 different options for free spot, therefore:
24*5=120

let's go back to the boys. remember the "free" spots? for every option with the "Free" sit, we can put 3 different boys to sit, and so the answer:
120*3 = 360

Waiting the OA
CEO
Joined: 12 Sep 2015
Posts: 2872
From a group of three boys and four girls, a school hallway monitor gr  [#permalink]

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Updated on: 08 Feb 2017, 09:28
Top Contributor
1
Bunuel wrote:
From a group of three boys and four girls, a school hallway monitor group is to be selected. If the group is to be formed of one boy and four girls, how many different such groups can be formed?

A. 1
B. 3
C. 36
D. 72
E. 360

Take the task of creating a hallway monitor group and break it into stages.

Stage 1: Select 4 girls to be in the group
Since there are only 4 girls to choose from, there's only 1 way to select 4 girls - you must select ALL of them, so there's only 1 way.
Alternatively, we COULD say that we can select 4 girls from the 4 girls in 4C4 ways (which also equals 1)
So, we can complete stage 1 in 1 way

Stage 2: Select 1 boy to be in the group
Since there are 3 boys to choose from, we can complete stage 2 in 3 ways

By the Fundamental Counting Principle (FCP), we can complete the two stages (and thus create a 4-person hallway monitor group) in (1)(3) ways (= 3 ways)

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn this technique.

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Originally posted by GMATPrepNow on 02 Feb 2017, 16:15.
Last edited by GMATPrepNow on 08 Feb 2017, 09:28, edited 1 time in total.
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Re: From a group of three boys and four girls, a school hallway monitor gr  [#permalink]

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03 Feb 2017, 02:12
Bunuel wrote:
From a group of three boys and four girls, a school hallway monitor group is to be selected. If the group is to be formed of one boy and four girls, how many different such groups can be formed?

A. 1
B. 3
C. 36
D. 72
E. 360

$$3c1$$ *$$4c4$$= $$3 * 1$$ = 3
Intern
Joined: 02 Feb 2017
Posts: 17
Concentration: Entrepreneurship, Strategy
Re: From a group of three boys and four girls, a school hallway monitor gr  [#permalink]

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03 Feb 2017, 22:09
Bunuel wrote:
From a group of three boys and four girls, a school hallway monitor group is to be selected. If the group is to be formed of one boy and four girls, how many different such groups can be formed?

A. 1
B. 3
C. 36
D. 72
E. 360

Since the question is asking number of group, then the answer is 3 (E)
3C1 x 4C4 = 3

If the question specifies in the group one of the captain will be selected, then the answer will be 72.
(3C1 X 4C4) x (1! x 4!) = 72
Thanks
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Re: From a group of three boys and four girls, a school hallway monitor gr  [#permalink]

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10 Apr 2017, 14:24
we have 3C1 * 4C4 = 3*1 = 3.

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Re: From a group of three boys and four girls, a school hallway monitor gr  [#permalink]

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03 Aug 2018, 15:46
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