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From 8 people, a team of 4 needs to be selected. How many ways are pos
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Updated on: 07 Jul 2021, 00:22
Updated on: 07 Jul 2021, 00:22
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From 8 people, a team of 4 needs to be selected. How many ways are possible if two particular people do not want to be together in the team?
(A) 35
(B) 55
(C) 40
(D) 60
(E) 75
(A) 35
(B) 55
(C) 40
(D) 60
(E) 75
From 8 people, a team of 4 needs to be selected. How many ways are pos
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07 Jul 2021, 00:26
07 Jul 2021, 00:26
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Expert Reply
SPHOORTHI wrote:
From 8 people, a team of 4 needs to be selected. How many ways are possible if two particular people do not want to be together in the team?
(A) 35
(B) 55
(C) 40
(D) 60
(E) 75
(A) 35
(B) 55
(C) 40
(D) 60
(E) 75
Say A and B do not want to be together in the team.
The number of teams with A but not B = 6C3 = 20 (we have A in the team and choosing the remaining 3 members out of 8 - A - B = 6)
The number of teams with B but not A = 6C3 = 20 (we have B in the team and choosing the remaining 3 members out of 8 - A - B = 6)
The number of teams without both A and B = 6C4 = 15 (choosing all 4 members from 8 - A - B = 6).
Total = 20 + 20 + 15 = 55.
Answer: B.
From 8 people, a team of 4 needs to be selected. How many ways are pos
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07 Jul 2021, 00:31
07 Jul 2021, 00:31
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Expert Reply
Bunuel wrote:
SPHOORTHI wrote:
From 8 people, a team of 4 needs to be selected. How many ways are possible if two particular people do not want to be together in the team?
(A) 35
(B) 55
(C) 40
(D) 60
(E) 75
(A) 35
(B) 55
(C) 40
(D) 60
(E) 75
Say A and B do not want to be together in the team.
The number of teams with A but not B = 6C3 = 20 (we have A in the team and choosing the remaining 3 members out of 8 - A - B = 6)
The number of teams with B but not A = 6C3 = 20 (we have B in the team and choosing the remaining 3 members out of 8 - A - B = 6)
The number of teams without both A and B = 6C4 = 15 (choosing all 4 members from 8 - A - B = 6).
Total = 20 + 20 + 15 = 55.
Answer: B.
OR:
The total number of teams possible = 8C4 = 70.
The number of teams with A and B = 6C2 = 15 (we have both A and B in the team and choosing the remaining 2 members out of 8 - A - B = 6).
The number of teams without A and B together = Total - Restriction = 70 - 15 = 55.
Answer: B.
