Discussion
In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
Answer: D
There are ten children. "At least one boy" is easiest through the complement.
\[ \text{total} = {}^{10}C_{4} = 210 \]
\[ \text{no boy} = {}^{4}C_{4} = 1 \]
\[ 210 - 1 = 209 \]
With only four girls there is exactly one all-girl selection, so the complement is a single case.
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