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?

  • A 15
  • B 28
  • C 30
  • D 45
jamb 2000mathematics

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 \(\binom{8}{3} - \binom{3}{3} - \binom{5}{3} = 56 - 1 - 10 = \boxed{45}\).

Previous question Next question