Discussion
Groups each containing 3 boys are to be formed out of 5 boys. A, B, C, D and E such that no group can contain both C and D together. What is the maximum number of such different groups?
Answer: C
Count all groups of three, then remove the forbidden ones.
\[ \text{total} = {}^{5}C_{3} = 10 \]
Groups containing both C and D need one more from A, B, E:
\[ {}^{3}C_{1} = 3 \]
\[ 10 - 3 = 7 \]
Counting the forbidden case and subtracting is quicker than enumerating the seven allowed groups directly.
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