Eight wires (all with different colors) need to be attached to a circuit board. A robotic device will attach the wires. The wires can be attached in any order, and the production manager wishes to determine which order would be fastest for the robot to use. Use the multiplication rule of counting to determine the number of possible sequences of assembly that must be tested.
A)40,320
B)64
C)8
D)36
E)none of these choices

Question

Quizplus · Accepted Answer

The multiplication rule states that the number of possible sequences of assembly is equal to the product of the number of choices for each step. In this case, there are 8 choices for the first step, 7 for the second (since one wire has already been attached), 6 for the third, and so on. Therefore, the total number of possible sequences is 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320.

Eight Wires (All with Different Colors) Need to Be Attached