Question

The number of ways in which $4n$ things can be divided into $4$ equal parts is

• A. $\frac{\left(4n\right)!}{4!(n!{)}^4}$
• B. $\frac{\left(4n\right)!}{(n!{)}^4}$
• C. $\frac{\left(4n\right)!}{4!(4{)}^n}$
• D. $\frac{\left(4n\right)!}{4!n!}$

Answer 1

The correct option is A $\frac{\left(4n\right)!}{4!(n!{)}^4}$

Given there are total $4n$ things.
Thus number of ways in which these things can be divided into four equal part is,
$=\frac{\left(4n\right)!}{n!n!n!n!.4!}=\frac{\left(4n\right)!}{4!.(n!{)}^4}$

The term $4!$ in the denominator is included because those 4 sets are indistinguishable.