From a group of three boys and four girls

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

From a group of three boys and four girls

by BTGmoderatorDC » Sun Jan 07, 2018 5:44 pm

From a group of three boys and four girls, a line of children from left to right is to be selected to salute the flag. If the line must have three boys and two girls, how many different such lines can be formed?

(A) 1,440
(B) 720
(C) 144
(D) 72
(E) 60

Can some experts show me the best solution in this problem?

OA B

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Source: Beat The GMAT — Problem Solving | Sun Jan 07, 2018 5:44 pm

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by GMATGuruNY » Mon Jan 08, 2018 3:50 am

lheiannie07 wrote:From a group of three boys and four girls, a line of children from left to right is to be selected to salute the flag. If the line must have three boys and two girls, how many different such lines can be formed?

(A) 1,440
(B) 720
(C) 144
(D) 72
(E) 60

The line must consist of 3 boys and 2 girls.
From the 3 boys, the number of ways to choose 3 = 3C3 = (3*2*1)/(3*2*1) = 1.
From the 4 girls, the number of ways to choose 2 = 4C2 = (4*3)/(2*1) = 6.
Number of ways to arrange the 5 selected children = 5! = 120.
To combine the options above, we multiply:
1*6*120 = 720.

The correct answer is B.

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by Scott@TargetTestPrep » Sun Aug 04, 2019 10:30 am

BTGmoderatorDC wrote:From a group of three boys and four girls, a line of children from left to right is to be selected to salute the flag. If the line must have three boys and two girls, how many different such lines can be formed?

(A) 1,440
(B) 720
(C) 144
(D) 72
(E) 60

Can some experts show me the best solution in this problem?

OA B

We need to determine the number of ways to line up 3 boys and 2 girls from 3 boys and 4 girls.

Let's first determine the number of ways to select the boys and girls.

The boys can be selected in 3C3 = 1 way.

The girls can be selected in 4C2 = 4!/[2!(4-2)!] = (4 x 3)/2! = 6 ways.

Thus, the total number of ways to select the boys and girls is 1 x 6 = 6.

We can arrange the 5 children in 5! = 120 ways.

Thus, the total number of ways in which we can select the group and arrange the children is 120 x 6 = 720 ways.

Answer: B

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