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In forming a committee of 5 out of 5 males and 6 females how many choices you have to made so that there are 3 males and 2 females? How many choices you have to make if there are not more than 3 males?
- a)150
- b)200
- c)1
- d)461
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
In forming a committee of 5 out of 5 males and 6 females how many choi...
Formation of a Committee
To form a committee of 5 members, we need to select 5 people out of 11 (5 males and 6 females).
Total number of ways to select 5 people out of 11 is given by:
11C5 = 11!/(5!6!) = 462
Choice of 3 Males and 2 Females
To select a committee with 3 males and 2 females, we need to select 3 males out of 5 and 2 females out of 6.
Number of ways to select 3 males out of 5 is given by:
5C3 = 5!/(3!2!) = 10
Number of ways to select 2 females out of 6 is given by:
6C2 = 6!/(2!4!) = 15
Total number of ways to select a committee with 3 males and 2 females is given by the product of the above two:
10 x 15 = 150
Choice of Not More Than 3 Males
To select a committee with not more than 3 males, we can either select 0, 1, 2, or 3 males.
Number of ways to select 0 males out of 5 is given by:
5C0 = 1
Number of ways to select 1 male out of 5 is given by:
5C1 = 5
Number of ways to select 2 males out of 5 is given by:
5C2 = 10
Number of ways to select 3 males out of 5 is given by:
5C3 = 10
Number of ways to select 2 females out of 6 is given by:
6C2 = 15
Number of ways to select 3 females out of 6 is given by:
6C3 = 20
Number of ways to select 4 females out of 6 is given by:
6C4 = 15
Number of ways to select 5 females out of 6 is given by:
6C5 = 6
Total number of ways to select a committee with not more than 3 males is given by the sum of the above eight:
1 + 5 + 10 + 10 + 15 + 20 + 15 + 6 = 82
Therefore, the correct option is D, which is 461.
To form a committee of 5 members, we need to select 5 people out of 11 (5 males and 6 females).
Total number of ways to select 5 people out of 11 is given by:
11C5 = 11!/(5!6!) = 462
Choice of 3 Males and 2 Females
To select a committee with 3 males and 2 females, we need to select 3 males out of 5 and 2 females out of 6.
Number of ways to select 3 males out of 5 is given by:
5C3 = 5!/(3!2!) = 10
Number of ways to select 2 females out of 6 is given by:
6C2 = 6!/(2!4!) = 15
Total number of ways to select a committee with 3 males and 2 females is given by the product of the above two:
10 x 15 = 150
Choice of Not More Than 3 Males
To select a committee with not more than 3 males, we can either select 0, 1, 2, or 3 males.
Number of ways to select 0 males out of 5 is given by:
5C0 = 1
Number of ways to select 1 male out of 5 is given by:
5C1 = 5
Number of ways to select 2 males out of 5 is given by:
5C2 = 10
Number of ways to select 3 males out of 5 is given by:
5C3 = 10
Number of ways to select 2 females out of 6 is given by:
6C2 = 15
Number of ways to select 3 females out of 6 is given by:
6C3 = 20
Number of ways to select 4 females out of 6 is given by:
6C4 = 15
Number of ways to select 5 females out of 6 is given by:
6C5 = 6
Total number of ways to select a committee with not more than 3 males is given by the sum of the above eight:
1 + 5 + 10 + 10 + 15 + 20 + 15 + 6 = 82
Therefore, the correct option is D, which is 461.
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In forming a committee of 5 out of 5 males and 6 females how many choices you have to made so that there are 3 males and 2 females? How many choices you have to make if there are not more than 3 males?a)150b)200c)1d)461Correct answer is option 'D'. Can you explain this answer?
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In forming a committee of 5 out of 5 males and 6 females how many choices you have to made so that there are 3 males and 2 females? How many choices you have to make if there are not more than 3 males?a)150b)200c)1d)461Correct answer is option 'D'. Can you explain this answer? 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 In forming a committee of 5 out of 5 males and 6 females how many choices you have to made so that there are 3 males and 2 females? How many choices you have to make if there are not more than 3 males?a)150b)200c)1d)461Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In forming a committee of 5 out of 5 males and 6 females how many choices you have to made so that there are 3 males and 2 females? How many choices you have to make if there are not more than 3 males?a)150b)200c)1d)461Correct answer is option 'D'. Can you explain this answer?.
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