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rxs0005
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From a group of three boys and four girls, a line of children from lef 22 Dec 2010, 16:38
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55% (hard)

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62% (01:42) correct 38% (02:00) wrong based on 249 sessions

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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
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B
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From a group of three boys and four girls, a line of children from lef 22 Dec 2010, 18:57
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rxs0005
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
Show more


Out of 3 boys and 4 girls, you need 3 boys and 2 girls
No of ways of selecting 3 boys out of 3 boys = 1
No of ways of selecting 2 girls out of 4 girls = 4C2 = 4*3/2 = 6
No of ways to arrange the 3 boys and 2 girls in a line = 5! = 120
Total number of arrangements = 6*120 = 720
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From a group of three boys and four girls, a line of children from lef 06 Jun 2017, 00:03
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Such kind of questions can be always done by first 'selecting' (combinations) then arranging (permutations).
Here we have to select 3 boys, 2 girls from 3 boys, 4 girls - and then arrange those 5 people in a straight line.

Selection of 3 boys (from 3 boys) and 2 girls (from 4 girls) = 3C3 * 4C2 = 1*6 = 6
Arrangement of 5 people selected in a straight line = 5! = 120

Total ways = 6*120 = 720.

Hence B answer
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From a group of three boys and four girls, a line of children from lef 08 Jun 2017, 16:47
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rxs0005
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
Show more

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 group of 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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From a group of three boys and four girls, a line of children from lef 20 Sep 2019, 11:38
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No of ways of selecting 3 boys out of 3 boys = 1
No of ways of selecting 2 girls out of 4 girls = \(4C2 = 6\)

No of ways to arrange the 3 boys and 2 girls in a line = 5! = 120

Total number of arrangements = 6*120 = 720

P.S: The question should say the line is of size 5. I understand it can be implicit but it can also mean that "Line is of 7 and there must be 3girls and 2 boys and you don't care about rest of the 2". At least that is what I feel.

Thank you!
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From a group of three boys and four girls, a line of children from lef 28 Jan 2025, 08:21
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