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A three-member committee has to be formed from a group of 9 people. How many such distinct committees can be formed?
- a)27
- b)72
- c)81
- d)84
Correct answer is option 'D'. Can you explain this answer?
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A three-member committee has to be formed from a group of 9 people. Ho...
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Explanation:
Step 1: Calculate the number of ways to choose a 3-member committee
- To form a committee of 3 members from a group of 9 people, we use the combination formula which is given by nCr = n! / r!(n-r)!
- In this case, n = 9 (total number of people) and r = 3 (number of members in the committee)
- Therefore, the number of ways to choose a 3-member committee = 9C3 = 9! / 3!(9-3)! = 84
Step 2: Determine the distinct committees that can be formed
- Once the 3 members are chosen for the committee, the order in which they are chosen does not matter. Therefore, the committees are considered distinct regardless of the order of selection.
- Hence, there are 84 distinct committees that can be formed from a group of 9 people.
Therefore, the correct answer is option D) 84.
Step 1: Calculate the number of ways to choose a 3-member committee
- To form a committee of 3 members from a group of 9 people, we use the combination formula which is given by nCr = n! / r!(n-r)!
- In this case, n = 9 (total number of people) and r = 3 (number of members in the committee)
- Therefore, the number of ways to choose a 3-member committee = 9C3 = 9! / 3!(9-3)! = 84
Step 2: Determine the distinct committees that can be formed
- Once the 3 members are chosen for the committee, the order in which they are chosen does not matter. Therefore, the committees are considered distinct regardless of the order of selection.
- Hence, there are 84 distinct committees that can be formed from a group of 9 people.
Therefore, the correct answer is option D) 84.
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A three-member committee has to be formed from a group of 9 people. How many such distinct committees can be formed?a)27b)72c)81d)84Correct answer is option 'D'. Can you explain this answer?
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