Question

Consider 23 different coloured beads in a necklace. In how many ways can the beads be placed in the necklace so that 3 specific beads always remain together?

Answer 1

By theory, let us consider 3 beads as one. Hence we have, in effect, 21 beads, n = 21.

The number of arrangements   1/2(n - 1)! = 1/220!

Also, the number of ways in which 3 beads can be arranged between themselves is 3! = 3 x 2 x1 = 6

 Thus, the total number of arrangements = (1/2) . 20! . 3!