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

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In a class of 10 students, a group of 4 will be selected for [#permalink] New post 19 Jun 2010, 08:59
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58% (02:22) correct 42% (01:54) wrong based on 79 sessions
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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Re: PS: Counting Methods [#permalink] New post 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?

Answers:
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).

Answer: A.

Hope it's clear.
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Kudos [?]: 11 [0], given: 2

Re: PS: Counting Methods [#permalink] New post 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?

Answers:
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).

Answer: A.

Hope it's clear.


Yes it is, sometimes i get very stuck with these questions. Thanks!
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Re: In a class of 10 students, a group of 4 will be selected for [#permalink] New post 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] New post 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
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Joined: 02 Sep 2009
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Kudos [?]: 49813 [1] , given: 7496

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

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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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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