Question

The number of ways in which $6$ Hindus, $2$ Muslims and $3$ Christians can be seated around a table such that people of same religion are always to be seated together

• A. $11!$
• B. $6!.2!.3!$
• C. $6!.2!.3{!}^2$
• D. $10!$

Answer 1

The correct option is C $6!.2!.3{!}^2$

$6$ Hindus is $1$ Unit

$2$ Muslims is $1$ Unit

$3$ Christan is $1$ Unit

Integral arrangement of each unit

$\Rightarrow 6!⟶1stunit\Rightarrow 2!⟶2ndunit\Rightarrow 3!⟶3rdunit$

Arrangements possible of $3$ Units

$=3!$

Total possible arrangements

$\Rightarrow 6!\times 2!\times 3!\times 3!\Rightarrow 6!\times 2!\times {(3!)}^2$