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A certain team consists of 4 professors and 6 teaching assistants. How

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A certain team consists of 4 professors and 6 teaching assistants. How [#permalink]

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A certain team consists of 4 professors and 6 teaching assistants. How many different teams of 3 can be formed in which at least one member of the group is a professor? (Two groups are considered different if at least one group member is different.)

A. 48
B. 100
C. 120
D. 288
E. 600
[Reveal] Spoiler: OA

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Re: A certain team consists of 4 professors and 6 teaching assistants. How [#permalink]

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New post 25 May 2016, 05:36
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The groups can be formed as
PTT + PPT + PPP where P=professor and T=Teaching assistant
Number of different teams of 3 can be formed in which at least one member of the group is a professor
= 4C1* 6C2 + 4C2*6C1 + 4C3
= 4!/3! * 6*5/2 + 4*3/2 * 6 + 4
=60 +36 + 4
=100

Answer B
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Re: A certain team consists of 4 professors and 6 teaching assistants. How [#permalink]

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New post 26 May 2016, 01:58
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Atleast one professor = Total - No professor

i.e, 10C3 - 6C3 = 120 -20 =100

ans : B

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Re: A certain team consists of 4 professors and 6 teaching assistants. How [#permalink]

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New post 26 May 2016, 09:14
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Bunuel wrote:
A certain team consists of 4 professors and 6 teaching assistants. How many different teams of 3 can be formed in which at least one member of the group is a professor? (Two groups are considered different if at least one group member is different.)

A. 48
B. 100
C. 120
D. 288
E. 600


At least one professor= Total possibility- All teaching assistants

Total possibility= 10C3= 120
Teaching assistant= 6C3= 20

AT least one professor= 120-20= 100

B is the answer
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Re: A certain team consists of 4 professors and 6 teaching assistants. How [#permalink]

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New post 26 May 2016, 10:03
Bunuel wrote:
A certain team consists of 4 professors and 6 teaching assistants. How many different teams of 3 can be formed in which at least one member of the group is a professor? (Two groups are considered different if at least one group member is different.)

A. 48
B. 100
C. 120
D. 288
E. 600


Number of different teams of 3 that can be formed in which at least one member of the group is a professor = Total Number of different teams of 3 that can be formed - Number of different teams of 3 that can be formed in which no member of the group is a professor
Total Number of different teams of 3 that can be formed = 10!/7!3! = 120
Number of different teams of 3 that can be formed in which no member of the group is a professor = 6!/3!3! = 20
Number of different teams of 3 that can be formed in which at least one member of the group is a professor = 120 - 20 = 100
Answer - B

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Re: A certain team consists of 4 professors and 6 teaching assistants. How [#permalink]

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Re: A certain team consists of 4 professors and 6 teaching assistants. How   [#permalink] 12 Oct 2017, 09:17
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