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A group of 10 people consists of 3 married couples and 4 single men. A

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A group of 10 people consists of 3 married couples and 4 single men. A [#permalink]

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A group of 10 people consists of 3 married couples and 4 single men. A committee of 4 is to be formed from the 10 people. How many different committees can be formed if the committee can consist of at most 1 married couple?

(A) 105
(B) 207
(C) 210
(D) 540
(E) 5,040
[Reveal] Spoiler: OA

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Re: A group of 10 people consists of 3 married couples and 4 single men. A [#permalink]

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New post 06 Jun 2016, 06:32
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Total number of possibilities of selecting 4 people out of 10 without any restrictions = 10C4 = 10!/(4!*6!)
= (10*9*8*7)/4*3*2*1
= 10*3*7
= 210
Number of possibilities of selecting 2 married couples = 3C2 = 3!/2! = 3
Number of different committees with atmost 1 married couple that can be formed = 210 - 3 = 207
Answer B
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Re: A group of 10 people consists of 3 married couples and 4 single men. A [#permalink]

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New post 05 Sep 2016, 22:59
Skywalker18 wrote:
Total number of possibilities of selecting 4 people out of 10 without any restrictions = 10C4 = 10!/(4!*6!)
= (10*9*8*7)/4*3*2*1
= 10*3*7
= 210
Number of possibilities of selecting 2 married couples = 3C2 = 3!/2! = 3
Number of different committees with atmost 1 married couple that can be formed = 210 - 3 = 207
Answer B


Shouldn't the possibilities of selecting 2 married couples be 4C2 here? Please explain.
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Re: A group of 10 people consists of 3 married couples and 4 single men. A [#permalink]

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New post 05 Sep 2016, 23:13
ranaazad wrote:
Skywalker18 wrote:
Total number of possibilities of selecting 4 people out of 10 without any restrictions = 10C4 = 10!/(4!*6!)
= (10*9*8*7)/4*3*2*1
= 10*3*7
= 210
Number of possibilities of selecting 2 married couples = 3C2 = 3!/2! = 3
Number of different committees with atmost 1 married couple that can be formed = 210 - 3 = 207
Answer B


Shouldn't the possibilities of selecting 2 married couples be 4C2 here? Please explain.


There are only 3 married couples. Number of ways 2 couples can be selected out of 3 is 3C2.

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Re: A group of 10 people consists of 3 married couples and 4 single men. A [#permalink]

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Re: A group of 10 people consists of 3 married couples and 4 single men. A [#permalink]

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New post 04 Oct 2017, 15:40
Bunuel wrote:
A group of 10 people consists of 3 married couples and 4 single men. A committee of 4 is to be formed from the 10 people. How many different committees can be formed if the committee can consist of at most 1 married couple?

(A) 105
(B) 207
(C) 210
(D) 540
(E) 5,040


If there are no restrictions on how to select the 4 people from a group of 10 people, then we have:

10C4 = 10!/[4!(10-4)!] = 10!/(4!6!) = (10 x 9 x 8 x 7)/4! = (10 x 9 x 8 x 7)/(4 x 3 x 2 x 1) = 5 x 3 x 2 x 7 = 210

ways to select them.

All of these ways will consist of at most 1 married couple, except if the 4 people picked consist of 2 married couples. So, let’s determine the number of ways 2 married couples can be picked as a committee of 4:

If a committee of 4 consists of 2 married couples, then it could be: (couple 1, couple 2), (couple 1, couple 3), or (couple 2, couple 3). Thus, there are only 3 ways 2 married couples can be picked for the committee of 4. Subtract this from 210 and we have 207 ways to select a committee of 4 that will consist of at most 1 married couple.

Answer: B
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Re: A group of 10 people consists of 3 married couples and 4 single men. A [#permalink]

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New post 01 Nov 2017, 00:15
Skywalker18 wrote:
Total number of possibilities of selecting 4 people out of 10 without any restrictions = 10C4 = 10!/(4!*6!)
= (10*9*8*7)/4*3*2*1
= 10*3*7
= 210
Number of possibilities of selecting 2 married couples = 3C2 = 3!/2! = 3
Number of different committees with atmost 1 married couple that can be formed = 210 - 3 = 207
Answer B


Why are we subtracting the number of married couple from total? Why not add them to 210? Would be happy to know the reasoning behind this:)

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Re: A group of 10 people consists of 3 married couples and 4 single men. A   [#permalink] 01 Nov 2017, 00:15
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