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14 Mar 2025, 00:30
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C
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Difficulty:
75%
(hard)
Question Stats:
55% (02:14) correct
45%
(02:31)
wrong
based on 174
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A group of twelve volunteers, including Ariel and Naja, are helping to organize a charity event. A committee consisting of a chair, vice-chair, secretary, and treasurer is made up of four volunteers randomly chosen from the twelve. What is the probability that Ariel is chosen as the chair of the committee, and Naja is also on the committee?
A. 1/11
B. 1/22
C. 1/44
D. 1/66
E. 1/132
A. 1/11
B. 1/22
C. 1/44
D. 1/66
E. 1/132
14 Mar 2025, 02:22
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No of ways the committee of \(4\) can be formed out of \(12 = 12*11*10*9\)
Since Ariel is chosen as the Chair, there are 3 positions remaining. So there are 3 ways where Ariel is the Chair and Naja is in the committee. Remaining 2 positions can be formed by choosing 2 out of remaining 10 volunteers in \(10*9\) ways
No of ways Ariel is the Chair and Naja in the committee \(=3*10*9\)
Probability of desired event \(= \frac{3*10*9}{12*11*10*9}=\frac{1}{44}\)
Answer: C
Since Ariel is chosen as the Chair, there are 3 positions remaining. So there are 3 ways where Ariel is the Chair and Naja is in the committee. Remaining 2 positions can be formed by choosing 2 out of remaining 10 volunteers in \(10*9\) ways
No of ways Ariel is the Chair and Naja in the committee \(=3*10*9\)
Probability of desired event \(= \frac{3*10*9}{12*11*10*9}=\frac{1}{44}\)
Answer: C
14 Mar 2025, 04:43
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Probability that Ariel is chosen as the chair of the committee = 1/12
Probability that Naja is also on the committee = 3/11
Probability of both events = 1/12 * 3/11 = 1/44
Probability that Naja is also on the committee = 3/11
Probability of both events = 1/12 * 3/11 = 1/44
Bunuel
