Groups each obtaining 3 boys are to be formed out of 5 boysA, 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?

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Q: 41 (IAS/2007)
Groups each obtaining 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?

question_subject: 

Logic/Reasoning

question_exam: 

IAS

stats: 

0,1,7,1,6,1,0

keywords: 

{'groups': [0, 0, 1, 0], 'maximum number': [1, 0, 1, 2], 'group': [0, 1, 0, 0], 'such different groups': [0, 0, 1, 0], 'boys': [0, 1, 5, 11]}

We aim to form groups of 3 boys in such a way that no group contains both boys C and D. This stipulation effectively means that we split our pool into two different sets:

1. Boys A, B, C, and E can form groups together.

2. Boys A, B, D, and E can form groups together.

Considering the first set (A, B, C, E), there are 4C3 (4 choose 3) = 4 ways to construct a valid group, because you are choosing 3 boys from a pool of 4.

Considering the second set (A, B, D, E), there are again 4C3 = 4 ways to construct a valid group using the same reasoning.

So the maximum number of groups is the sum of these two possibilities, which is 4 + 4 = 8. Therefore, the provided answer is incorrect.

Alert - the correct answer should be 8.