From the 12 male and 8 female sales representatives for an insurance company, a team of 4 men and 4 women will be selected to attend a national conference on insurance fraud. Requried:
In how many ways can the team of 6 representatives be selected?

Total ways = ¹²C₄ × ⁸C₄

Total ways = 495 × 70

Total ways = 34,650

Therefore, there are 34,650 ways to select a team of 4 men and 4 women from 12 male and 8 female sale representatives.

Step-by-step explanation:

From the given information,

There are 12 male sales representatives

There are 8 female sales representatives

We want to select a team of 4 men and 4 women

Requried:

In how many ways can the team of 6 representatives be selected?

There must be a typing error since it is given in the question that 4 men and 4 women are to be selected.

4 + 4 = 8

So the correct question is

In how many ways can the team of 8 representatives be selected?

A team of 4 men from 12 men may be selected as

Men = ¹²C₄ = 495 ways

A team of 4 women from 8 women may be selected as

Women = ⁸C₄ = 70 ways

So the team of 8 representatives may be selected as

Total ways = ¹²C₄ × ⁸C₄

Total ways = 495 × 70

Total ways = 34,650

Therefore, there are 34,650 ways to select a team of 4 men and 4 women from 12 male and 8 female sale representatives.