Discussion

What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?

Answer: C

One particular man and one particular woman are fixed in the group, so only the rest are free to choose.

\[ \text{2 more men from the remaining 4} = {}^{4}C_{2} = 6 \]

\[ \text{1 more woman from the remaining 5} = {}^{5}C_{1} = 5 \]

\[ 6 \times 5 = 30 \]

Fixing members always reduces both the pool and the number still to be chosen.

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