Groups each containing 3 boys are to be formed out of 5 boys - A, B,C, D and E such that no one
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 such different groups?
(a) 5 (b) 6 (c) 7 (d) 8
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(c) Total number of arrangements, when any 3 boys are selected out of 5 = 5C3. Now, when groups contains both C and D, then their selection is fixed and the remaining 1 boy can be selected out of the remaining 3 boys. It can be done in 3C1 ways.
So, number of groups, when none contains both C and D = total number of arrangements-number of arrangements when group contains both C and D
= 5C3 – 3C1
= 10 – 3 = 7
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