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From a group of three boys and four girls, a school hallway monitor gr
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31 Jan 2017, 09:04

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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?

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31 Jan 2017, 15:18

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)

Answer is B;

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

From a group of three boys and four girls, a school hallway monitor gr
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Updated on: 08 Feb 2017, 08:28

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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)

Answer: B

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, 15:15.
Last edited by GMATPrepNow on 08 Feb 2017, 08:28, edited 1 time in total.

Re: From a group of three boys and four girls, a school hallway monitor gr
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03 Feb 2017, 01:12

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?

Re: From a group of three boys and four girls, a school hallway monitor gr
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03 Feb 2017, 21:09

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

Re: From a group of three boys and four girls, a school hallway monitor gr
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03 Aug 2018, 14:46

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