Ordering a five-song set list

Question

A DJ has chosen 5 distinct songs and must decide the order to play them. How many different set lists (orderings) are possible?

Accepted Answer

Choose the songs position by position. The first slot can be any of the 5 songs, the second any of the 4 that remain, then 3, then 2, then the last one is forced: 5 	imes 4 	imes 3 	imes 2 	imes 1 = 5! = 120. Every distinct ordering is counted once, because once you fix which song is first, second, and so on, the whole set list is determined. Takeaway. Ordering n distinct items gives n! arrangements. Five songs yield 5! = 120 set lists.

Ordering a five-song set list

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