Question

Eight beads are strung in a necklace with a clasp, how many ways
can the beads be arranged?

Answer 1

Number of total arrangement of beads = 2,520

Explanation:

Given:

Number of beads in necklace = 8 beads

Find:

Number of total arrangement of beads

Computation:

Changing beads is a cyclic permutation,

So,

Formula to find number of total arrangement in cyclic permutation

(n-1)!/2 , where n = number of item

So,

(n-1)!/2

Number of total arrangement of beads = (8-1)!/2

Number of total arrangement of beads = (7)!/2

Number of total arrangement of beads = (7 x 6 x 5 x 4 x 3 x 2 x 1) / 2

Number of total arrangement of beads = 5,040 / 2

Number of total arrangement of beads = 2,520