Three research departments have 8,6,7 members, respectively. Each department is to select a delegate and an alternate to represent the department at a conference. In how many ways can this be done

70,560 ways

Step-by-step explanation:

This problem is an arrangement problem, as the order of the two people chose in each department matters.

So, for each department, we have an arrangement:

First department: arrange of 8 choose 2: A (8,2) = 8!/2! = 8*7 = 56

Second department: arrange of 6 choose 2: A (6,2) = 6!/2! = 6*5 = 30

Third department: arrange of 7 choose 2: A (7,2) = 7!/2! = 7*6 = 42

The total number of ways is the product of each number of arranges, so:

Number of ways = 56 * 30 * 42 = 70,560