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From a group of three boys and four girls, a line of children arranged

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From a group of three boys and four girls, a line of children arranged [#permalink]

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New post 27 Apr 2017, 01:17
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From a group of three boys and four girls, a line of children arranged from left to right is to be selected to salute the flag. If exactly two children are in the line, how many different such lines can be formed?

A. 76
B. 42
C. 21
D. 12
E. 7
[Reveal] Spoiler: OA

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From a group of three boys and four girls, a line of children arranged [#permalink]

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New post 27 Apr 2017, 02:55
There are 3 options to form this line
All boys form this line
3c2 = 3

All girls form this line
4c2 = 6

One boy and one girl form this line
3c1 * 4c1 = 3*4 = 12

Total number of options = 3+6+12 = 21(Option C)
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Last edited by pushpitkc on 04 May 2017, 23:27, edited 2 times in total.
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Re: From a group of three boys and four girls, a line of children arranged [#permalink]

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New post 04 May 2017, 23:15
From a group of three boys and four girls, a line of children arranged from left to right is to be selected to salute the flag. If exactly two children are in the line, how many different such lines can be formed?

A. 76
B. 42
C. 21
D. 12
E. 7

This is a question o arrangement so 7C1 * 6C1 = 42
Ans = B
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From a group of three boys and four girls, a line of children arranged [#permalink]

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New post 04 May 2017, 23:31
pushpitkc wrote:
There are 3 options to form this line
All boys form this line
3c2 = 3

All girls form this line
4c2 = 6

One boy and one girl form this line
3c1 * 4c1 = 3*4 = 12

Total number of options = 3+6+12 = 21(Option C)


Missed this part of the solution
As there are 2 ways of arranging the people in the line,
the different type of lines that can be formed are 2*21 = 42(Option B)
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From a group of three boys and four girls, a line of children arranged [#permalink]

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New post 06 May 2017, 17:30
Basically, I don't care if there are boys or girls in that line. I just see them as 7 people. Gender is not important here.

Plus, the order matters in that case because they said "a line of children arranged from left to right".

So I used the permutation formula: 7! / (7-2)! = 42.

Answer is B
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Re: From a group of three boys and four girls, a line of children arranged [#permalink]

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New post 07 May 2017, 02:33
three boys and four girls= 7 people
available 2 spots
1st spot=7 choice
2nd spot=6 choice
total possible arrangement= 7*6=42
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Re: From a group of three boys and four girls, a line of children arranged [#permalink]

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New post 07 May 2017, 05:14
People have provided good explanations for solving this sum. I'd like to give the easiest method to solve the given question in less than 20 seconds.

Since we have been asked about "arrangement", we need to consider 2 different arrangements for each pair of students. (If we were asked about number of possible combinations, we could have used 7C2.

However, in the given question, the operative word is Arrangement. In 90% of the cases, we use the formula for Permutations when asked about "Arrangement"

Hence, the answer will be 7P2 = 7!/(7-2)! = 7!/5! = 42.
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Re: From a group of three boys and four girls, a line of children arranged [#permalink]

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New post 07 May 2017, 05:36
Order matters, irrespective of gender. So 7 people can be arranged in 7p2 ways... 42.

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Re: From a group of three boys and four girls, a line of children arranged   [#permalink] 07 May 2017, 05:36
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