Question

From a group of 20 day workers and 12 night workers, a skeleton work crew of 5 day workers and 3 night workers must be formed. in how many ways can this be done

Answer 1

3,410,880 ways.

Explanation:

There are no markings to differentiate the position so the order is not important. The group also divided into day and night workers which independent from each other.

You want to make a schedule for 5 day workers out of 20 day workers, the number of ways to do that will be: 5C20= 20!/5!15! =15504 ways

You want to make a schedule for 3 night workers out of 12 night workers, the number of ways to do that will be: 3C12= 12!/3!9! =220 ways

The total number of ways possible will be 15504 * 220 = 3410880 ways.