Discussion
A box contains 2 white, 3 black and 5 red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?
Answer: D
There are \( 2 + 3 + 5 = 10 \) balls, 7 of them not black. Use the complement.
\[ \text{total} = {}^{10}C_{3} = 120 \]
\[ \text{no black} = {}^{7}C_{3} = 35 \]
\[ 120 - 35 = 85 \]
Counting one, two and three black balls separately gives \( 3 \times 21 + 3 \times 7 + 1 = 85 \) as well.
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