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# In a class of 10 students, a group of 4 will be selected for

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Intern
Joined: 30 May 2010
Posts: 30
Schools: YALE SOM
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In a class of 10 students, a group of 4 will be selected for [#permalink]

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19 Jun 2010, 08:59
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59% (02:23) correct 41% (01:48) wrong based on 109 sessions

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In a class of 10 students, a group of 4 will be selected for a trip. How many different groups are possible, if 2 of those 10 students are a married couple and will only travel together?

A. 98
B. 115
C. 122
D. 126
E. 165
[Reveal] Spoiler: OA
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Posts: 36540
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Kudos [?]: 93039 [2] , given: 10541

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19 Jun 2010, 09:18
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Nusa84 wrote:
In a class of 10 students, a group of 4 will be selected for a trip. How many different groups are possible, if 2 of those 10 students are a married couple and will only travel together?

A. 98
B. 115
C. 122
D. 126
E. 165

I keep getting the wrong answer all the time ...

Thanks

We can have either two married students plus two other students or 4 students out of 8 (no married student among them).

$$C^1_1*C^2_{8}+C^4_{8}=28+70=98$$.
$$C^1_1$$ - # of ways to choose 1 couple out of 1 couple;
$$C^2_{8}$$ - # of ways to choose 2 students out of 8 left (10 - 2 married=8);
$$C^4_{8}$$ - # of ways to choose 4 student out of 8 (so not to choose any married student).

Hope it's clear.
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Joined: 30 May 2010
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Schools: YALE SOM
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Kudos [?]: 18 [0], given: 2

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19 Jun 2010, 09:36
Bunuel wrote:
Nusa84 wrote:
In a class of 10 students, a group of 4 will be selected for a trip. How many different groups are possible, if 2 of those 10 students are a married couple and will only travel together?

A. 98
B. 115
C. 122
D. 126
E. 165

I keep getting the wrong answer all the time ...

Thanks

We can have either two married students plus two other students or 4 students out of 8 (no married student among them).

$$C^1_1*C^2_{8}+C^4_{8}=28+70=98$$.
$$C^1_1$$ - # of ways to choose 1 couple out of 1 couple;
$$C^2_{8}$$ - # of ways to choose 2 students out of 8 left (10 - 2 married=8);
$$C^4_{8}$$ - # of ways to choose 4 student out of 8 (so not to choose any married student).

Hope it's clear.

Yes it is, sometimes i get very stuck with these questions. Thanks!
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Kudos [?]: 24 [2] , given: 10

Re: In a class of 10 students, a group of 4 will be selected for [#permalink]

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16 Apr 2014, 21:09
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We need to break the grouping down to 2 scenarios : with the married couple or without the married couple in the group of 4 people for the trip

1) With the married couple in the group, we have to find the number of possibilities for the other 2 spots in the group from the left 8 people = 8!/(2!*6!) = 28
2) Without the married couple in the group, we have to find the number of possibilities for picking 4 people from the 8 unmarried people from the group = 8!/(4! * 4! ) = 70

Total number of possibilities = 28 + 70 = 98 (A)
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In a class of 10 students, a group of 4 will be selected for a trip. [#permalink]

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06 Apr 2015, 09:51
In a class of 10 students, a group of 4 will be selected for a trip. How many different groups are possible, if 2 of those 10 are a married couple and will only travel together?

a) 98

b) 115

c) 122

d) 126

e) 165
Math Expert
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Posts: 36540
Followers: 7072

Kudos [?]: 93039 [1] , given: 10541

Re: In a class of 10 students, a group of 4 will be selected for [#permalink]

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06 Apr 2015, 09:54
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Expert's post
Awli wrote:
In a class of 10 students, a group of 4 will be selected for a trip. How many different groups are possible, if 2 of those 10 are a married couple and will only travel together?

a) 98

b) 115

c) 122

d) 126

e) 165

Merging similar topics. Please refer to the discussion above.
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Re: In a class of 10 students, a group of 4 will be selected for   [#permalink] 06 Apr 2015, 09:54
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