Answer:
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