Question

In how many ways can five counters labeled A, B, C, D, and E at a store be staffed by two men and three women chosen from a group of four men and six women?

a. 60
b. 120
c. 240
d. 360

Answer 1

To staff five counters with two men chosen from four and three women chosen from six, we calculate the combinations separately and multiply the results to get a total of 120 ways.

Step-by-step explanation:

The question asks for the number of ways to staff five counters with two men and three women from a group of four men and six women. This is a problem of counting combinations because the order in which the men and women are chosen does not matter.

The number of ways to choose two men out of four is given by the combination formula which is C(n, k) = n! / (k!(n - k)!), where n is the total number of people to choose from (in this case, men), and k is the number of people to choose. Thus, for the men, we have C(4, 2) = 4! / (2!(4 - 2)!) = 6 ways.

Similarly, for choosing three women out of six, the number of ways is C(6, 3) = 6! / (3!(6 - 3)!) = 20 ways.

To find the total number of ways to choose the two men and three women, we multiply the two numbers of outcomes. Hence, the total number of ways is 6 x 20 = 120.