Question

From the 10 male and 8 female sales representatives for an insurance​ company, a team of 4 men and 3 women will be selected to attend a national conference on insurance fraud.

In how many ways can the team of 7 be​ selected

Answer 1

We have to find in how many ways can the team of 7 be selected if we choose 4 men from the 10 and 3 women from the 8:
n = 4C10 * 3C8 =
= [( 10 * 9 * 8 * 7 ) / ( 4 * 3 * 2 * 1 )]  *  [( 8 * 7 * 6 ) / ( 3 * 2 * 1 )] =
= 5040 / 24    *  336 / 6  = 210 * 56 = 11,760
Answer:
The team of 7 can be selected in 11,760 ways.