Suppose that we have five round beads, coloured red, blue, green, violet, and go

Question

Suppose that we have five round beads, coloured red, blue, green, violet, and golden. We want to string them into a bracelet.

(a) We start by lining them up along a string. How many ways can we do this?

(b) Once we’ve tied the string into a loop, the beads can rotate freely along the string; we can also flip the bracelet around. Given this, how many different bracelets can we make?

(c) In the context of (b), suppose that we don’t want to have the green and the blue beads next to each other. Now how many bracelets are possible?

Explanation / Answer

a) factorial 5 =120 ( we can permutate 5 objects in factorial ways)

b) (factorial 4)/2 ( we need arrange 5 things in circle this can be done in factorial (5-1)/2 ways)

c) total - green and blue together

60- 3

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