Question

In how many ways can 10 different beads be arranged to form a necklace
​

Answer 1

Answer:

This is called a cyclic permutation. The formula for this is simply (n-1)!/2, since all the beads are identical. Hence, the answer is 9!/2 = 362880/2 = 181440....

Answer 2

The beads can be arranged in 1,81,440 ways.

Given:

Number of beads=10

To find:

The number of ways in which these can be arranged in a necklace

Solution:

The number of arrangements required can be obtained by using the following formula.

The number of beads in the necklace, n=10

The total ways of arranging these beads =(n-1)!/2

Using the value of n,

=(10-1)!/2

=9!/2

=(9×8×7×6×5×4×3×2×1)/2

=9×8×7×6×5×4×3×1

=72×42×60

=1,81,440

Therefore, the beads can be arranged in 1,81,440 ways.