Question

In how many ways can you divide these cards in four sets, three of them having 17 cards each and the fourth one just one card?

• A. $\frac{52!}{(17!{)}^{3}1!(3!{)}^3}$
• B. $\frac{52!}{(17!{)}^3}$
• C. $\frac{52!}{(17!{)}^{3}1!3!}$
• D. $\frac{52!}{(17!)(3!)}$

Answer 1

The correct option is C $\frac{52!}{(17!{)}^{3}1!3!}$

the number of ways of dividing two cards into four sets
$=[{}^{52}{C}_{17}{\times }^{35}{C}_{17}{\times }^{18}{C}_{17}\times 1]\times \frac{1}{3!}$
$=\frac{52!}{35!\times 17!}\times \frac{35!}{18!\times 17!}\times \frac{18!}{17!\times 1!}\times 1!\times \frac{1}{3!}$
$=\frac{52!}{(17!{)}^3\times 3!}$