Stringing eight distinct beads in a line

Question

You thread 8 distinct beads onto a straight wire, one after another, forming a line (there is a definite left end and right end, so the wire is not a loop). In how many different orders can the beads be strung?

Accepted Answer

Because the wire is a straight line with a fixed left-to-right direction, this is an ordinary arrangement of 8 distinct objects. Place beads from the left: 8 choices for the first, 7 for the next, and so on: 8! = 8 	imes 7 	imes 6 	imes 5 	imes 4 	imes 3 	imes 2 	imes 1 = 40320. (Note: if the wire were closed into a loop, rotations would coincide and the count would be smaller. On a straight line every position is distinguishable, so the full factorial applies.) Takeaway. Arranging n distinct objects along a line with a fixed direction gives n!. Eight beads give 8! = 40320.

Stringing eight distinct beads in a line

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