Question

Find the number of ways in which $12$ different beads can be arranged to form a necklace.

• A. $\frac{1}{2}(11!)$
• B. $11!$
• C. $\frac{1}{2}(12!)$
• D. $12!$

Answer 1

The correct option is A $\frac{1}{2}(11!)$

$12$ different beads can be arranged among themselves in a circular
order in $(12-1)!=11!$ ways. Now in the case of necklace,
there is no distinction between clockwise and anticlockwise
arrangements.
So the required number of arrangements = $\frac{1}{2}(11!)$