Question

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

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

Answer 1

Answer: (C)

$4!$

For all the keys to be arranged in a row,

Number of arrangements $=5!$

$\because$ there are groups of 5 arrangements.

$\therefore$ Total number of arrangements in a row $=\frac{5!}{5}=\frac{4!\times 5}{5}=4!$

Hence, there are a total $4!$ no. of ways in which 5 keys can be put in a ring