Please help I have been working on this one problem for days. From the 9 male and 6 female representatives for an insurance company, a team of 4 men and 4 women will be selected to attend a conference on insurance fraud.How many ways can a team of 8 be selected?
so we are "choosing" 4 men from 9 and 4 women from 6
Number of ways = C(9,4) x C(6,4)
= 126(15) = 1890
There are C(9,4) ways to choose the men, and C(6,4) ways to choose the women.
So, there are C(9,4)*C(6,4) = 1890 ways to choose the committee.
To calculate the number of ways a team of 8 can be selected from 9 men and 6 women, you can use the concept of combinations. The formula for combinations is given by:
C(n, r) = n! / (r!(n - r)!)
Where:
- n is the total number of objects in the group
- r is the number of objects to be chosen from the group
- n! denotes the factorial of n, which is the product of all positive integers less than or equal to n
In this case, we want to select 4 men out of 9 and 4 women out of 6 to form a team of 8. So we can calculate the number of ways as follows:
C(9, 4) * C(6, 4) = (9! / (4!(9 - 4)!)) * (6! / (4!(6 - 4)!))
= (9! / (4!5!)) * (6! / (4!2!))
= (9 * 8 * 7 * 6!) / (4! * 5!) * (6! / (4! * 2!))
= (9 * 8 * 7) / (4 * 3 * 2 * 1) * (6 * 5)
= (9 * 8 * 7 * 6 * 5) / (4 * 3 * 2 * 1 * 4 * 2)
= (9 * 7 * 5) / (3 * 2)
= 63
Therefore, there are 63 ways to select a team of 8, consisting of 4 men and 4 women, from the given representatives.