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# A treasure hunt competition requires a team of 4 students.

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Intern
Joined: 11 Oct 2017
Posts: 22

Kudos [?]: 6 [0], given: 82

A treasure hunt competition requires a team of 4 students. [#permalink]

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09 Nov 2017, 18:15
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Difficulty:

65% (hard)

Question Stats:

45% (01:57) correct 55% (01:33) wrong based on 33 sessions

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A treasure hunt competition requires a team of 4 students. There are 6 students who are willing to participate: John, Edward, Milner, Luiz, Howard and Paul. However, Edward and Milner do not want to be on a team together, while Paul only wants to be on a team if Edward is also. How many different teams can be formed?

A. 3
B. 6
C. 5
D. 7
E. 8

[Reveal] Spoiler: OA

Kudos [?]: 6 [0], given: 82

Manager
Joined: 24 Jun 2017
Posts: 118

Kudos [?]: 14 [0], given: 129

A treasure hunt competition requires a team of 4 students. [#permalink]

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09 Nov 2017, 19:20
Edward and Milner is a constrain
just ecxlude one of them, so 5 ways only 5C4

Last edited by cbh on 09 Nov 2017, 19:32, edited 1 time in total.

Kudos [?]: 14 [0], given: 129

Math Expert
Joined: 02 Aug 2009
Posts: 5339

Kudos [?]: 6103 [0], given: 121

Re: A treasure hunt competition requires a team of 4 students. [#permalink]

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09 Nov 2017, 19:24
A treasure hunt competition requires a team of 4 students. There are 6 students who are willing to participate: John, Edward, Milner, Luiz, Howard and Paul. However, Edward and Milner do not want to be on a team together, while Paul only wants to be on a team if Edward is also. How many different teams can be formed?

A. 3
B. 6
C. 5
D. 7
E. 8

two CASES:-

1) when E is there
M will not be there
now two subcases
a) with P
choose 2 out of remaining 3 = 3C2=3
b) without P
only three remaining and all three are to be chosen = 3C3=1

2) when M is there
E and therefore P cannot be there..
Only 3 remaining and all 3 are to be chosen = 1

total $$3+1+1=5$$
C
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6103 [0], given: 121

Intern
Joined: 16 Feb 2017
Posts: 27

Kudos [?]: 14 [1], given: 80

Re: A treasure hunt competition requires a team of 4 students. [#permalink]

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09 Nov 2017, 20:52
1
KUDOS
A treasure hunt competition requires a team of 4 students. There are 6 students who are willing to participate: John, Edward, Milner, Luiz, Howard and Paul. However, Edward and Milner do not want to be on a team together, while Paul only wants to be on a team if Edward is also. How many different teams can be formed?

A. 3
B. 6
C. 5
D. 7
E. 8

Total ways to make a team - 6C4 = 15
Unwanted 1 Scenario (where E&M are together) - 4C2 = 6
Unwanted 2 Scenario (where either of P or E are on team) - 4C3 = 4

Desired = 15-6-4 = 5

Hope this helps!

Kudos [?]: 14 [1], given: 80

Re: A treasure hunt competition requires a team of 4 students.   [#permalink] 09 Nov 2017, 20:52
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