Question

In how many ways can 5 keys be put in a ring.

• A. $\frac{1}{2}4!$
• B. $\frac{1}{2}5!$
• C. $4!$
• D. $5!$

Answer 1

Answer: (A)

$\frac{1}{2}4!$

Answer 2

Required number of ways = $\frac{1}{2}(5 - 1)\mspace{6mu}! = \frac{4\mspace{6mu}!}{2}$.

{Since clockwise and anticlockwise are same in case of ring}.