In how many ways can we pick 1 woman and 2 men from groups of a: 8 men and 7 women, b. 3 men and 3 women?

1 Answer

#a => 196, b=>9#

Explanation:

This is a combinations question - we don't care in what order the committees are selected.

The general formula for combinations is:

#C_(n,k)=(n!)/((k!)(n-k)!)# with #n="population", k="picks"#

We're picking 1 woman and 2 men from different sized pools:

a

men = 8, women = 7:

#C_(8,2)xxC_(7,1)=(8!)/((2!)(6!))xx(7!)/((1!)(6!))#

#(8xx7xx6!)/((2)(6!))xx(7xx6!)/((1)(6!))#

#28xx7=196# ways

b

men = 3, women = 3:

#C_(3,2)xxC_(3,1)=(3!)/((2!)(1!))xx(3!)/((1!)(2!))#

#(3xx2!)/((2!)(1))xx(3xx2!)/((1)(2!))#

#3xx3=9# ways