Question

Committee of five people is selected from 12 men and 6 women. In how many ways can the committee be chosen?

Answer 1

Number of ways to chosen 5 committee members from 12 men and 6 women 

= ¹²C₅ ⁶C₀ + ¹²C₄ . ⁶C₁ + 12C₃ . ⁶C₂ + ¹²C₂ . ⁶C₃ + ¹²C₁ . ⁶C₄ + ¹²C₀ . ⁶C₅

= \(\cfrac{12.11.10.9.8.7!}{7!\times5.4.3.2.1}\times1\) + \(\cfrac{12.11.10.9.8!}{8!\times4.3.2.1}\times6\) 

+ \(\cfrac{12.11.10.9!}{9!\times3.2.1}\times\cfrac{6\times5}2\) + \(\cfrac{12.11}2\) x \(\cfrac{6.5.4}{3.2.1}\) + 12 x \(\cfrac{6.5.4!}{4!\times2.1}\) + 1 x 6

= 798 + 2970 + 3300 + 1320 + 180 + 6

= 8574