Groups each containing 3 boys are to be formed out of 5 boys-A, B, C, D and E such that
no one group contains both C and D together. What is the maximum number of different groups?
a. 5
b. 6
c. 7
d. 8
Answers
Answer : (c) 7
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SOLUTION :
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Given that : There are some groups and each group containing 3 boys are to formed out of 5 boys named : A, B, C, D, and E
So, the way of finding total groups which containing 3 boys are to be formed from 5 boys :
By the formula of Combination we know that : nCr , where n = 5 ( total boys ), r = 3 ( boys are contained by each group ) and C = Combination
As we know that by the formula of combination :
nCr = n!/r! (n-r)!
On putting the value in the formula :
=> 5C3 = 5!/3!.(5-3)!
=> 5C3 = 5!/3!.2!
=> 5C3 = (5×4)/(2×1)
=> 5C3 = 10
But, there is also given that no one group contains C and D together, So, the group in which C and D together are :
(C,D,A), (C,D,B) and (C,D,E) = 3
The number of groups which doesn't contain C and D together = 10-3 = 7
So, the number of groups will be 7 which doesn't contain C and D together.
Therefore, the answer will be 7