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A committee of five is to be chosen from a group of 9 people. The probability that a certain married couple will either serve together or not at all is
- a)1/ 2
- b)5/ 9
- c)4/ 9
- d)2/ 3
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A committee of five is to be chosen from a group of 9 people. The prob...
The total number of ways in which 5 person can be chosen out of 9 person is 9C5 = 126
The couple serves the committee in 7C3 x 2C2 = 35 ways
The couple does not serve the committee in
7C5 - 7C2 = 21 ways
Since the couple will either be together or not at all
∴ favourable number of cases = 35 + 21 = 56
∴ required porbability = 56 126 = 4/9
The couple serves the committee in 7C3 x 2C2 = 35 ways
The couple does not serve the committee in
7C5 - 7C2 = 21 ways
Since the couple will either be together or not at all
∴ favourable number of cases = 35 + 21 = 56
∴ required porbability = 56 126 = 4/9
Most Upvoted Answer
A committee of five is to be chosen from a group of 9 people. The prob...
Probability of the married couple serving together or not at all
To calculate the probability that a certain married couple will either serve together or not at all in a committee of 5 chosen from 9 people, we need to consider the following scenarios:
Scenario 1: Married couple serves together
- If the married couple serves together in the committee, then there are 7 remaining people to choose from for the other 3 spots.
- The number of ways to choose the other 3 people from the remaining 7 is given by 7 choose 3 = 35.
Scenario 2: Married couple does not serve at all
- If the married couple does not serve at all in the committee, then both the husband and wife are not chosen.
- In this case, we need to choose all 5 members from the remaining 7 people, which can be done in 7 choose 5 = 21 ways.
Total number of ways to form the committee
- The total number of ways to form a committee of 5 from 9 people is given by 9 choose 5 = 126.
Calculating the probability
- The probability that the married couple will either serve together or not at all is the sum of the probabilities of the two scenarios calculated above, divided by the total number of ways to form the committee.
- Therefore, the probability = (35 + 21) / 126 = 56 / 126 = 4 / 9.
Therefore, the correct answer is option 'c) 4/9'.
To calculate the probability that a certain married couple will either serve together or not at all in a committee of 5 chosen from 9 people, we need to consider the following scenarios:
Scenario 1: Married couple serves together
- If the married couple serves together in the committee, then there are 7 remaining people to choose from for the other 3 spots.
- The number of ways to choose the other 3 people from the remaining 7 is given by 7 choose 3 = 35.
Scenario 2: Married couple does not serve at all
- If the married couple does not serve at all in the committee, then both the husband and wife are not chosen.
- In this case, we need to choose all 5 members from the remaining 7 people, which can be done in 7 choose 5 = 21 ways.
Total number of ways to form the committee
- The total number of ways to form a committee of 5 from 9 people is given by 9 choose 5 = 126.
Calculating the probability
- The probability that the married couple will either serve together or not at all is the sum of the probabilities of the two scenarios calculated above, divided by the total number of ways to form the committee.
- Therefore, the probability = (35 + 21) / 126 = 56 / 126 = 4 / 9.
Therefore, the correct answer is option 'c) 4/9'.
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A committee of five is to be chosen from a group of 9 people. The probability that a certain married couple will either serve together or not at all isa)1/ 2b)5/ 9c)4/ 9d)2/ 3Correct answer is option 'C'. Can you explain this answer?
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