Question

Find the number of ways in which $5$ persons $A,B,C,D,E$ can be seated at a round table such that $C$ and $D$ must not sit together?

• A. $24$
• B. $12$
• C. $6$
• D. $36$

Answer 1

Answer: (B)

$12$

$A,B,C,D,E$

Number of circular arrangements of $n$ circular objects $=(n-1)!$

Arrangement of $5$ people $=4!$ ways $=24$ ways

Let $C,D$ be together always

$\Rightarrow$ $C,D$ or $D,C$ $⟶$ $2!$ Ways

Arrangements of $4$ units $=3!\times 2$ Ways $=12$ Ways

Total arrangements such that $C$and$D$ are not together

$=24-12$ $=12$ Ways