Discussion
A committee has 5 men and 6 women. What are the number of ways of selecting a group of eight persons?
Answer: A
There are \( 5 + 6 = 11 \) people, and eight are to be chosen with no restriction on the mix.
\[ {}^{11}C_{8} = {}^{11}C_{3} = \frac{11 \times 10 \times 9}{6} = 165 \]
Choosing 8 to include is the same as choosing 3 to leave out, which makes the arithmetic much lighter.
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