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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?
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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 solve this problem, we need to use the concept of combination. Let's break down the problem into small steps:
Step 1: Selecting 3 ladies out of 8
We can select 3 ladies out of 8 in 8C3 ways. (nCr represents the number of ways of selecting r items from n items)
Step 2: Selecting 4 gents out of 7
We can select 4 gents out of 7 in 7C4 ways.
Step 3: Total number of committees
The total number of committees can be formed by multiplying the number of ways we can select ladies and gents i.e., 8C3 * 7C4.
Step 4: Excluding committees with Mr. Y and Mrs. X
Now, we need to exclude the committees in which Mr. Y and Mrs. X are together. Let's assume that Mr. Y is a member of the committee. In this case, we need to select 2 more gents from the remaining 6 gents (excluding Mr. Y) in 6C2 ways. Also, we need to select 3 ladies from the remaining 7 ladies (excluding Mrs. X) in 7C3 ways. Hence, the total number of committees with Mr. Y and Mrs. X together is 6C2 * 7C3.
Similarly, if we assume that Mrs. X is a member of the committee, then the total number of committees with Mr. Y and Mrs. X together is 7C2 * 8C3.
Step 5: Final answer
The final answer is the total number of committees excluding the committees with Mr. Y and Mrs. X i.e., 8C3 * 7C4 - 6C2 * 7C3 - 7C2 * 8C3 = 1520.
Therefore, the correct option is (c) 1520.
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 solve this problem, we need to use the concept of combination. Let's break down the problem into small steps:
Step 1: Selecting 3 ladies out of 8
We can select 3 ladies out of 8 in 8C3 ways. (nCr represents the number of ways of selecting r items from n items)
Step 2: Selecting 4 gents out of 7
We can select 4 gents out of 7 in 7C4 ways.
Step 3: Total number of committees
The total number of committees can be formed by multiplying the number of ways we can select ladies and gents i.e., 8C3 * 7C4.
Step 4: Excluding committees with Mr. Y and Mrs. X
Now, we need to exclude the committees in which Mr. Y and Mrs. X are together. Let's assume that Mr. Y is a member of the committee. In this case, we need to select 2 more gents from the remaining 6 gents (excluding Mr. Y) in 6C2 ways. Also, we need to select 3 ladies from the remaining 7 ladies (excluding Mrs. X) in 7C3 ways. Hence, the total number of committees with Mr. Y and Mrs. X together is 6C2 * 7C3.
Similarly, if we assume that Mrs. X is a member of the committee, then the total number of committees with Mr. Y and Mrs. X together is 7C2 * 8C3.
Step 5: Final answer
The final answer is the total number of committees excluding the committees with Mr. Y and Mrs. X i.e., 8C3 * 7C4 - 6C2 * 7C3 - 7C2 * 8C3 = 1520.
Therefore, the correct option is (c) 1520.
Community Answer
A committee of 3 ladies and 4 gents is to be formed out of 8 ladies an...
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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?
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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? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about 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? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
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? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about 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? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
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