Question

The number of ways in which $52$ cards can be divided into $4$ sets of $13$ each is

• A. $\frac{52!}{(13!{)}^4}$
• B. $\frac{52!}{4!(13!{)}^4}$
• C. $\frac{52!}{4^{13}}$
• D. $\frac{52!}{13!4^{13}}$

Answer 1

The correct option is B $\frac{52!}{4!(13!{)}^4}$

Total number of cards $=4\times 13=52$
Assuming all the cards are of different type.
Required number of ways is $=\frac{52!}{13!.13!.13!.13!.4!}=\frac{52!}{(13!{)}^{4}4!}$