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A committee of 3 men and 4 women is to be selected from 6 men and 9 women. If there is married couple among the 15 persons, in how many ways can the committee be selected so that it contains the married couple? a) 120 b) 32 c) 320 d) none of these?
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A committee of 3 men and 4 women is to be selected from 6 men and 9 wo...
Problem:
A committee of 3 men and 4 women is to be selected from 6 men and 9 women. If there is a married couple among the 15 persons, in how many ways can the committee be selected so that it contains the married couple?
Solution:
To solve this problem, we need to consider the different cases where the married couple can be included in the committee.
Case 1: Both the husband and wife are selected in the committee.
We need to select 1 man and 4 women from the remaining 5 men and 9 women. The number of ways to do this is given by:
C(5, 1) * C(9, 4) = 5 * 126 = 630
Case 2: Only the husband is selected in the committee.
We need to select 3 men and 4 women from the remaining 5 men and 9 women. The number of ways to do this is given by:
C(5, 3) * C(9, 4) = 10 * 126 = 1260
Case 3: Only the wife is selected in the committee.
We need to select 3 men and 4 women from the remaining 5 men and 9 women. The number of ways to do this is also 1260, as it is the same as Case 2.
Total number of ways:
To find the total number of ways to select the committee, we add the number of ways from each case:
Total number of ways = 630 + 1260 + 1260 = 3150
Therefore, the committee can be selected in 3150 ways so that it contains the married couple.
Answer:
The correct option is d) none of these.
A committee of 3 men and 4 women is to be selected from 6 men and 9 women. If there is a married couple among the 15 persons, in how many ways can the committee be selected so that it contains the married couple?
Solution:
To solve this problem, we need to consider the different cases where the married couple can be included in the committee.
Case 1: Both the husband and wife are selected in the committee.
We need to select 1 man and 4 women from the remaining 5 men and 9 women. The number of ways to do this is given by:
C(5, 1) * C(9, 4) = 5 * 126 = 630
Case 2: Only the husband is selected in the committee.
We need to select 3 men and 4 women from the remaining 5 men and 9 women. The number of ways to do this is given by:
C(5, 3) * C(9, 4) = 10 * 126 = 1260
Case 3: Only the wife is selected in the committee.
We need to select 3 men and 4 women from the remaining 5 men and 9 women. The number of ways to do this is also 1260, as it is the same as Case 2.
Total number of ways:
To find the total number of ways to select the committee, we add the number of ways from each case:
Total number of ways = 630 + 1260 + 1260 = 3150
Therefore, the committee can be selected in 3150 ways so that it contains the married couple.
Answer:
The correct option is d) none of these.
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A committee of 3 men and 4 women is to be selected from 6 men and 9 women. If there is married couple among the 15 persons, in how many ways can the committee be selected so that it contains the married couple? a) 120 b) 32 c) 320 d) none of these?
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A committee of 3 men and 4 women is to be selected from 6 men and 9 women. If there is married couple among the 15 persons, in how many ways can the committee be selected so that it contains the married couple? a) 120 b) 32 c) 320 d) none of these? for CA Foundation 2025 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 men and 4 women is to be selected from 6 men and 9 women. If there is married couple among the 15 persons, in how many ways can the committee be selected so that it contains the married couple? a) 120 b) 32 c) 320 d) none of these? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A committee of 3 men and 4 women is to be selected from 6 men and 9 women. If there is married couple among the 15 persons, in how many ways can the committee be selected so that it contains the married couple? a) 120 b) 32 c) 320 d) none of these?.
A committee of 3 men and 4 women is to be selected from 6 men and 9 women. If there is married couple among the 15 persons, in how many ways can the committee be selected so that it contains the married couple? a) 120 b) 32 c) 320 d) none of these? for CA Foundation 2025 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 men and 4 women is to be selected from 6 men and 9 women. If there is married couple among the 15 persons, in how many ways can the committee be selected so that it contains the married couple? a) 120 b) 32 c) 320 d) none of these? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A committee of 3 men and 4 women is to be selected from 6 men and 9 women. If there is married couple among the 15 persons, in how many ways can the committee be selected so that it contains the married couple? a) 120 b) 32 c) 320 d) none of these?.
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