Answer:
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.
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.