Question

There are nine wires which 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. (Hint: There are nine choices for the first wire, eight for the second wire, seven for the third wire, etc.)

Answer 1

When robot attached first wire , it has 9 choices, for second wire it has 8 choices, for third wire it has 7 choices, for fourth wire it has 6 choices, for fifth wire it has 5 choices, for sixth wire it has 4 choices, for seventh wire it has 3 choices, for eigth wire it has 2 choices and for ninth wire it has 1 choice. So by the multiplication rule of counting, the number of possible sequences of assembly that must be tested is

$9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1=362,880$