Question

From the 11

male and 6

female sales representatives for an insurance​ company, a team of 3

men and 2

women will be selected to attend a national conference on insurance fraud.
In how many ways can the team of 5

be​ selected?

Answer 1

Selecting r objects out of n objects, can be done in C(n, r) many ways.

For example selecting groups of 4 people out of 10 people can be done in
C(10, 4) many ways.


C(n, r) is calculated as follows: $C(n, r)= \frac{n!}{r!(n-r!)}$, 

where n! is 1*2*3*...*(n-1)*n


3 men out of 11 men, and 2 women out of 6 women are to be selected.

This can be done in C(11, 3) and C(6,2) ways respectively.

Since any of the selected men group can be combined with any of the selected women group, there are C(11, 3)*C(6,2) many ways of selecting the team of 5.


$C(11, 3)*C(6,2) = \frac{11!}{8!3!} * \frac{6!}{4!2!}= \frac{11*10*9*8!}{8!*3!}* \frac{6*5*4!}{4!*2!}= \frac{11*10*9}{3*2*1} * \frac{6*5}{2*1}=$

165*15=2475


Answer: 2475