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 ways
B) 120 ways
C) 10 ways
D) 15 ways

Answer 1

To staff five counters with two men and three women chosen from four men and six women, we calculate the combination of choosing two men (4C2 = 6 ways) and three women (6C3 = 20 ways) independently. By multiplying these together (6 x 20), we find there are 120 ways to staff the counters.

Step-by-step explanation:

The question is asking to calculate the number of ways to choose two men from a group of four and three women from a group of six to staff five counters. To find this number, we use the combination formula, which tells us how many ways we can choose a subset from a larger set without considering the order.

To choose two men from four, we calculate the number of combinations by using the formula 4C2, which equals 6 ways. Likewise, to choose three women from six, we calculate the number of combinations by using the formula 6C3, which equals 20 ways.

Since these choices are independent, we multiply the number of ways to choose the men by the number of ways to choose the women to get our final answer. So, we have 6 ways to choose the men and 20 ways to choose the women, giving us 6 x 20 = 120 ways to staff the five counters with two men and three women.

The correct answer is therefore B) 120 ways.