Hello, D. Martin!

How many bracelets can be made by putting six different-coloured beads

on a ring if 10 different colours are available?

Attempted Solution: Since there are 10 possible colours and you must arrange six of them,

I thought I should just use the permutation formula: .

Since the bracelet may be flipped over, I then divided the answer by 2 to obtain 75,600.

Good! . . . Most of us forget that.

But the correct answer is 12,600.

Since the beads are in a circle, an arrangement of 6 beads can be rotated

. . without creating another bracelet.

. . . . . . . . . .

. . . . . . . . . .

These six bracelets are identical . . . So your answer is too large by a factor of 6.