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Seven 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.

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DeanR

Answer:

The number of permutations of seven things, which is the number of different orders seven different wires can be connected, is 7!.

That's 7×6×5×4×3×2×1=5040

That's because there's 7 choices for the first wire, then 6 left for the second wire, 5 choices for the third, etc.  The multiplication rule of counting says we multiply all these for the final count.

Answer: 5040

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