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A team of 12 men is to be formed out of n persons. It is found that ‘A’ and ‘B’ are three times as often together as ‘C’ ‘D’ and ‘E’ are. Then the value of n is __________.
- a)32
- b)23
- c)9
- d)None
Correct answer is option 'A'. Can you explain this answer?
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A team of 12 men is to be formed out of n persons. It is found that &l...
The number of ways of forming the team is equal to the number of ways of forming a team of n-12 persons.
This can be explained using the concept of combinations. The number of ways of selecting k items from a set of n items is given by the combination formula:
C(n,k) = n!/((n-k)!k!)
In this case, the number of ways of forming a team of 12 men from n persons is given by:
C(n,12) = n!/((n-12)!12!)
And the number of ways of forming a team of n-12 persons is given by:
C(n,n-12) = n!/((n-(n-12))!(n-12)!) = n!/12!(n-12)!
Since the two expressions are equal, we can set them equal to each other and simplify:
n!/((n-12)!12!) = n!/12!(n-12)!
Canceling out the common terms, we get:
(n-12)! = 12!(n-12)!
Dividing both sides by (n-12)!, we get:
1 = 12!
This is a contradiction, since 12! is not equal to 1. Therefore, there is no solution for n, and the problem is ill-posed.
This can be explained using the concept of combinations. The number of ways of selecting k items from a set of n items is given by the combination formula:
C(n,k) = n!/((n-k)!k!)
In this case, the number of ways of forming a team of 12 men from n persons is given by:
C(n,12) = n!/((n-12)!12!)
And the number of ways of forming a team of n-12 persons is given by:
C(n,n-12) = n!/((n-(n-12))!(n-12)!) = n!/12!(n-12)!
Since the two expressions are equal, we can set them equal to each other and simplify:
n!/((n-12)!12!) = n!/12!(n-12)!
Canceling out the common terms, we get:
(n-12)! = 12!(n-12)!
Dividing both sides by (n-12)!, we get:
1 = 12!
This is a contradiction, since 12! is not equal to 1. Therefore, there is no solution for n, and the problem is ill-posed.
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A team of 12 men is to be formed out of n persons. It is found that ‘A’ and ‘B’ are three times as often together as ‘C’ ‘D’ and ‘E’ are. Then the value of n is __________.a)32b)23c)9d)NoneCorrect answer is option 'A'. Can you explain this answer?
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