From a group of three boys and four girls . .

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Mon Nov 06, 2017 6:52 am

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 two boys and three girls, how many different such groups can be formed?

A. 3
B. 4
C. 12
D. 72
E. 144

The OA is C.

How could I determine the possibilities? With permutations?

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Source: Beat The GMAT — Problem Solving | Mon Nov 06, 2017 6:52 am

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ErikaPrepScholar: Legendary Member; Posts: 503; Joined: Thu Jul 20, 2017 9:03 amFollowed by: 15 members; Thanked: 86 times; GMAT Score:770

by ErikaPrepScholar » Mon Nov 06, 2017 9:15 am

Let's find the number of possibilities for just boys and just girls first.

Boys: 3, choose 2
$$\frac{3!}{2!}=3$$

Girls: 4, choose 3
$$\frac{4!}{3!}=4$$

So there are 3 possible groups of boys and 4 possible groups of girls. Now, any of these groups of boys can be paired with any of these groups of girls.So the total number of possibilities is 3 * 4 = 12.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Nov 10, 2017 9:36 am

M7MBA 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 two boys and three girls, how many different such groups can be formed?

A. 3
B. 4
C. 12
D. 72
E. 144

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

Stage 1: Select two boys for the group
Since the order in which we select the boys does not matter, we can use combinations.
We can select 2 boys from 3 boys in 3C2 ways (3 ways)
So, we can complete stage 1 in 3 ways

If anyone is interested, we have a free video on calculating combinations (like 3C2 or 11C2) in your head: https://www.gmatprepnow.com/module/gmat- ... /video/789

Stage 2: Select two girls for the group
We can select 3 girls from 4 girls in 4C3 ways (4 ways)
So, we can complete stage 2 in 4 ways

By the Fundamental Counting Principle (FCP), we can complete the two stages (and thus create the hallway monitor group) in (3)(4) ways (= 12 ways)

Answer: C
--------------------------

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat- ... /video/775

You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat ... /video/776

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Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8139; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Oct 31, 2019 5:16 pm

M7MBA 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 two boys and three girls, how many different such groups can be formed?

A. 3
B. 4
C. 12
D. 72
E. 144

The OA is C.

How could I determine the possibilities? With permutations?

The number of groups that can be formed is:

3C2 x 4C3 = 3 x 4 = 12

Answer: C

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Founder and CEO
[email protected]

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