In how many ways can a delegation of 3 be chosen from among 5 men and 3 women, if at least one man and at least one woman must be included?
The correct answer is D. 45
The otal number of ways to choose a delegation of 3 from among 5 men and 3 women is \(\binom{8}{3}\).
The number of ways to choose a delegation of 3 without any men is \(\binom{3}{3}\), and the number of ways to choose a delegation of 3 without any women is \(\binom{5}{3}\).
So, the number of ways to choose a delegation of 3 with at least one man and at least one woman is \(\binom{8}{3} - \binom{3}{3} - \binom{5}{3} = 56 - 1 - 10 = \boxed{45}\).
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