Question

The numbers of ways in which a pack of 52 cards can be divided equally among four players in orders is

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

Answer 1

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

If $4n$ different things are to be equally distributed amongst $4$ persons the numbers of ways are

$\frac{4n!}{(n!{)}^4}$ but if $4n$ things are to form $4$ equal groups then

the numbers of ways are $\frac{4n!}{(n!{)}^4\times 4!}$

Number of ways of dividing $52$ cards equally among $4$ players $=\frac{52!}{(13!{)}^4\times 4!}$