Question

From the 6 male and 11 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? . . . question content area right part 1 in how many ways can the team of 5 representatives be​ selected?

Answer 1

Using combinations, we calculate there are 1100 ways to select a team of 3 men and 2 women from 6 male and 11 female representatives.

Step-by-step explanation:

We're asked to determine the number of ways a team of 5 representatives can be selected from 6 male and 11 female representatives, with the team consisting of 3 men and 2 women. To solve this, we will need to use combinations, which are used to find the number of ways to choose a group from a larger set where order does not matter.

First, we calculate the number of ways to choose 3 men out of 6. This is done using the combination formula: C(n, k) = n! / (k! * (n - k)!), where n is the total number of items, k is the number of items to choose, and ! denotes factorial.

For the men: C(6, 3) = 6! / (3! * (6 - 3)!) = 20.

Similarly, for the women: C(11, 2) = 11! / (2! * (11 - 2)!) = 55.

To find the total number of combinations, we multiply the two results together since each combination of 3 men can be paired with any combination of 2 women: 20 * 55 = 1100.

Therefore, there are 1100 ways the team of 5 representatives can be selected.