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18 Feb 2024, 05:46
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E
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Difficulty:
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Question Stats:
82% (01:40) correct
18%
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wrong
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If a club has 12 members, what is the ratio of the number of different possible 6-member committees that can be formed to the number of different possible 5-member committees that can be formed?
A: 7 to 1
B: 6 to 1
C: 7 to 5
D: 6 to 5
E: 7 to 6
A: 7 to 1
B: 6 to 1
C: 7 to 5
D: 6 to 5
E: 7 to 6
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18 Feb 2024, 05:53
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Manuel2504
The number of 6-member committees that can be formed from 12 memebers is 12C6 = 12!/(6!6!)
The number of 5-member committees that can be formed from 12 memebers is 12C5 = 12!/(7!5!)
The ratio, thus is
- \(\frac{\frac{12!}{6!6!}}{\frac{12!}{7!5!}} = \)
\(=\frac{12!}{6!6!} * \frac{7!5!}{12!}=\)
\(=\frac{7}{6}\)
Answer: E.
18 Feb 2024, 07:15
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Manuel2504
Asked: If a club has 12 members, what is the ratio of the number of different possible 6-member committees that can be formed to the number of different possible 5-member committees that can be formed?
Number of possible 6-member committees = 12C6 = 12!/6!6!
Number of possible 5-member committees = 12C5 = 12!/5!7!
The ratio of the number of different possible 6-member committees that can be formed to the number of different possible 5-member committees that can be formed = (12!/6!6!)/(12!/5!7!) = 7/6
IMO E
Asked: If a club has 12 members, what is the ratio of the number of different possible 6-member committees that can be formed to the number of different possible 5-member committees that can be formed?
Number of possible 6-member committees = 12C6 = 12!/6!6!
Number of possible 5-member committees = 12C5 = 12!/5!7!
The ratio of the number of different possible 6-member committees that can be formed to the number of different possible 5-member committees that can be formed = (12!/6!6!)/(12!/5!7!) = 7/6
IMO E
