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Juliette [100K]
3 years ago
15

A committee of 5 people is to be chosen from a group of 8 women and 10 men. How many diffferent committees are possible? How man

y are possible if the committee must feature both men and women? How many are possible if the committee must feature 3 women and 2 men? How many are possible if the committee must have more women than men?
Mathematics
1 answer:
Jet001 [13]3 years ago
3 0
A) 5 to be chosen among a Total : 10 Men + 8 Women

¹⁸C₅ = (18!)/(5!)(13!) = 8,568 groups of five

b) A must to have men and women. If so we have to deduct all groups of 5 that are all men and all group of 5 that are all women
Groups of 5 with only men: ¹⁰C₅ = 252
Groups of 5 with only women: ⁸C₅ = 56

So number of committees of 5 men and women mixed =
8568 - 252 - 56 = 8,260 committees 

c) 3 Women and 2 Men:

⁸C₃ x ¹⁰C₂ = 2,520 groups of 3 W and 2 M

d) More women than men, it means:
  3 W + 2 M OR (we have found it in c) = 2,520)
  4 W + 1 M OR   ⁸C₄ x ¹⁰C₁   →→→→ =    700
  5 W + 0 M OR   ⁸C₅ x ¹⁰C₀   →→→→  =     56

Total where W>M = 3,276 groups of 5 where women are at least 3


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