Discussion
In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?
Answer: C
The men and the women are chosen from separate pools, so the counts multiply.
\[ {}^{8}C_{5} \times {}^{10}C_{6} \]
\[ = 56 \times 210 = 11{,}760 \]
Using \( {}^{8}C_{3} \) and \( {}^{10}C_{4} \) gives the same values, since choosing whom to include is equivalent to choosing whom to leave out.
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