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19 Aug 2024, 01:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
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Question Stats:
65% (01:32) correct
35%
(01:52)
wrong
based on 231
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There are 7 executives, including the CEO and CFO, that are asked to form a small team of 5 members. However, the CEO and CFO may not both be assigned to the team. Given this constraint, how many ways are there to form the team?
A. 6
B. 10
C. 11
D. 21
E. 28
A. 6
B. 10
C. 11
D. 21
E. 28
19 Aug 2024, 01:59
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Workout the total ways of selecting 5 people from 7, then subtract the number of ways the CEO and CFO will be together in the team to find the answer.
Total ways of selecting 5 people from 7: \(\frac{7!}{5!2!} = 21\)
Number of ways the CEO and CFO will be together in the team: The CEO and CFO will take up two spots in the team, therefore it's a matter of choosing 3 from the 5 other executives: \(\frac{5!}{3!2!}= 10\)
How many ways are there to form the team with the constraints given: \(21 - 10 = 11\)
ANSWER C
Total ways of selecting 5 people from 7: \(\frac{7!}{5!2!} = 21\)
Number of ways the CEO and CFO will be together in the team: The CEO and CFO will take up two spots in the team, therefore it's a matter of choosing 3 from the 5 other executives: \(\frac{5!}{3!2!}= 10\)
How many ways are there to form the team with the constraints given: \(21 - 10 = 11\)
ANSWER C
19 Aug 2024, 02:29
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Total no. of ways to form a committee = 7C5 => 21
No. of ways to form a committee with both CEO and CFO together in the committee = 5C3 => 10
No. of ways to form a committee without both CEO and CFO together in the committee = Total - Both Together => 7C5 - 5C3 => 11
Therefore, answer is C. 11
No. of ways to form a committee with both CEO and CFO together in the committee = 5C3 => 10
No. of ways to form a committee without both CEO and CFO together in the committee = Total - Both Together => 7C5 - 5C3 => 11
Therefore, answer is C. 11
