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A committee of 3 ladies and 4 gents is to be formed out of 8 ladies and 7 gents. Mrs. X refuses to serve in a committee in which Mr. Y is a member. The number of such committees is
- a)1530
- b)1500
- c)1520
- d)1540
Correct answer is option 'D'. Can you explain this answer?
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A committee of 3 ladies and 4 gents is to be formed out of 8 ladies an...
Problem Statement:
A committee of 3 ladies and 4 gents is to be formed out of 8 ladies and 7 gents. Mrs. X refuses to serve in a committee in which Mr. Y is a member. The number of such committees is:
Solution:
To form a committee of 3 ladies and 4 gents out of 8 ladies and 7 gents, we need to select 3 ladies out of 8 and 4 gents out of 7. The number of ways to do this is given by:
Number of ways to select 3 ladies out of 8 = 8C3 = (8*7*6)/(3*2*1) = 56
Number of ways to select 4 gents out of 7 = 7C4 = (7*6*5*4)/(4*3*2*1) = 35
The total number of ways to form a committee of 3 ladies and 4 gents is:
Total number of ways = 56 * 35 = 1960
Now, we need to subtract the number of committees in which Mrs. X and Mr. Y are both members. Let us denote the number of such committees by N.
To form a committee of 3 ladies and 4 gents out of 8 ladies and 7 gents, in which Mrs. X and Mr. Y are both members, we need to select 2 ladies out of 7 (excluding Mrs. X) and 3 gents out of 6 (excluding Mr. Y). The number of ways to do this is given by:
Number of ways to select 2 ladies out of 7 = 7C2 = (7*6)/(2*1) = 21
Number of ways to select 3 gents out of 6 = 6C3 = (6*5*4)/(3*2*1) = 20
The total number of ways to form a committee of 3 ladies and 4 gents, in which Mrs. X and Mr. Y are both members, is:
N = 21 * 20 = 420
Therefore, the number of committees in which Mrs. X and Mr. Y are not both members is:
Total number of ways - N = 1960 - 420 = 1540
Hence, the correct option is (d) 1540.
A committee of 3 ladies and 4 gents is to be formed out of 8 ladies and 7 gents. Mrs. X refuses to serve in a committee in which Mr. Y is a member. The number of such committees is:
Solution:
To form a committee of 3 ladies and 4 gents out of 8 ladies and 7 gents, we need to select 3 ladies out of 8 and 4 gents out of 7. The number of ways to do this is given by:
Number of ways to select 3 ladies out of 8 = 8C3 = (8*7*6)/(3*2*1) = 56
Number of ways to select 4 gents out of 7 = 7C4 = (7*6*5*4)/(4*3*2*1) = 35
The total number of ways to form a committee of 3 ladies and 4 gents is:
Total number of ways = 56 * 35 = 1960
Now, we need to subtract the number of committees in which Mrs. X and Mr. Y are both members. Let us denote the number of such committees by N.
To form a committee of 3 ladies and 4 gents out of 8 ladies and 7 gents, in which Mrs. X and Mr. Y are both members, we need to select 2 ladies out of 7 (excluding Mrs. X) and 3 gents out of 6 (excluding Mr. Y). The number of ways to do this is given by:
Number of ways to select 2 ladies out of 7 = 7C2 = (7*6)/(2*1) = 21
Number of ways to select 3 gents out of 6 = 6C3 = (6*5*4)/(3*2*1) = 20
The total number of ways to form a committee of 3 ladies and 4 gents, in which Mrs. X and Mr. Y are both members, is:
N = 21 * 20 = 420
Therefore, the number of committees in which Mrs. X and Mr. Y are not both members is:
Total number of ways - N = 1960 - 420 = 1540
Hence, the correct option is (d) 1540.
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A committee of 3 ladies and 4 gents is to be formed out of 8 ladies and 7 gents. Mrs. X refuses to serve in a committee in which Mr. Y is a member. The number of such committees isa)1530b)1500c)1520d)1540Correct answer is option 'D'. Can you explain this answer?
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