Discussion
In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs. In how many ways can Raj choose 3 chairs so that at least one yellow chair is included?
Answer: C
There are \( 2 + 3 + 4 = 9 \) chairs. "At least one yellow" is easiest through the complement.
\[ \text{total} = {}^{9}C_{3} = 84 \]
\[ \text{no yellow} = {}^{6}C_{3} = 20 \]
\[ 84 - 20 = 64 \]
Counting exactly one, two and three yellows separately gives \( 3 \times 15 + 3 \times 6 + 1 = 64 \) as well - the same answer for three times the work.
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