Lining up six trophies on a shelf

Question

You have 6 distinct trophies and want to display them in a single row on a shelf. In how many different left-to-right orders can they be arranged?

Accepted Answer

Fill the shelf positions one at a time, left to right. Any of the 6 trophies can go first. Once placed, 5 remain for the second spot, then 4, and so on down to the last position: 6 	imes 5 	imes 4 	imes 3 	imes 2 	imes 1 = 6! = 720. This shrinking product is exactly the factorial n!, the number of ways to order n distinct objects. Each position uses up one trophy, so the choices decrease by one each step. Takeaway. The number of orderings of n distinct objects in a row is n!. For 6 trophies that is 6! = 720.

Lining up six trophies on a shelf

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