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A treasure hunt competition requires a team of 4 students.

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

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New post 09 Nov 2017, 17:15
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  65% (hard)

Question Stats:

57% (02:33) correct 43% (02:16) wrong based on 76 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


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

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New post Updated on: 09 Nov 2017, 18:32
Edward and Milner is a constrain
just ecxlude one of them, so 5 ways only 5C4

Originally posted by cbh on 09 Nov 2017, 18:20.
Last edited by cbh on 09 Nov 2017, 18:32, edited 1 time in total.
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Re: A treasure hunt competition requires a team of 4 students.  [#permalink]

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New post 09 Nov 2017, 18:24
ladyrenee95 wrote:
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


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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 \(3+1+1=5\)
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Re: A treasure hunt competition requires a team of 4 students.  [#permalink]

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New post 09 Nov 2017, 19:52
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ladyrenee95 wrote:
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


Ready4GMAT app


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

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New post 28 Feb 2018, 10:31
Edward In, Miller Out, Paul Out:
total combo = 1 * 3c3 = 1

Paul In, Edward MUST be in, Miller Out:
total combo = 3c2 = 3

No Edward, so No Paul, Miller In:
total combo = 3c3 = 1

total = 5
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Re: A treasure hunt competition requires a team of 4 students.   [#permalink] 28 Feb 2018, 10:31
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A treasure hunt competition requires a team of 4 students.

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