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From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
- a)624
- b)702
- c)756
- d)812
Correct answer is option 'C'. Can you explain this answer?
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From a group of 7 men and 6 women, five persons are to be selected to ...
Yes, its a permutation and combi ation question.
th question says atleast 3 men that means we can take 3 ,4 ,5 as our variant and among the women it will be 2 ,1 and 0.
(7C3 × 6C2)+(7C4 × 6C1)+(7C5 × 6C0)= 756
th question says atleast 3 men that means we can take 3 ,4 ,5 as our variant and among the women it will be 2 ,1 and 0.
(7C3 × 6C2)+(7C4 × 6C1)+(7C5 × 6C0)= 756
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From a group of 7 men and 6 women, five persons are to be selected to ...
Given: 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee.
To find: The number of ways to form a committee.
Approach: We can use the combination formula to solve this problem.
The number of ways to select a committee with at least 3 men would be the sum of the number of ways to select 3, 4, or 5 men and the remaining women.
Number of ways to select a committee with 3 men and 2 women = (7C3) × (6C2) = 35 × 15 = 525
Number of ways to select a committee with 4 men and 1 woman = (7C4) × (6C1) = 35 × 6 = 210
Number of ways to select a committee with 5 men and 0 women = (7C5) × (6C0) = 21 × 1 = 21
The total number of ways to form a committee with at least 3 men = 525 + 210 + 21 = 756.
Therefore, the correct option is (c) 756.
To find: The number of ways to form a committee.
Approach: We can use the combination formula to solve this problem.
The number of ways to select a committee with at least 3 men would be the sum of the number of ways to select 3, 4, or 5 men and the remaining women.
Number of ways to select a committee with 3 men and 2 women = (7C3) × (6C2) = 35 × 15 = 525
Number of ways to select a committee with 4 men and 1 woman = (7C4) × (6C1) = 35 × 6 = 210
Number of ways to select a committee with 5 men and 0 women = (7C5) × (6C0) = 21 × 1 = 21
The total number of ways to form a committee with at least 3 men = 525 + 210 + 21 = 756.
Therefore, the correct option is (c) 756.
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From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?a)624b)702c)756d)812Correct answer is option 'C'. Can you explain this answer?
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