Groups each containing 3 boys are to be formed out of 5 boys-,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?

To find the total number of groups of 3 boys that can be formed from a total of 5 boys, we use the combination formula 5C3. This equals 10 possible groups. The condition states that C and D cannot be in the same group. Therefore, we must identify and subtract the groups where C and D are together. If C and D are both in a group of 3, the third member must be either A, B, or E. This results in exactly 3 groups where C and D are together: 1. C, D, and A 2. C, D, and B 3. C, D, and E To find the maximum number of valid groups, subtract these 3 restricted groups from the total of 10. 10 minus 3 equals 7. Thus, the maximum number of such different groups is 7. The correct option is C.