Question

The number of ways in which $52$ cards can be divided into $4$ sets, three of them having $17$ cards each and the fourth one having just one card

• A. $\frac{52!}{(17!{)}^3}$
• B. $\frac{52!}{(17!{)}^{3}3!}$
• C. $\frac{51!}{(17!{)}^3}$
• D. $\frac{51!}{(17!{)}^{3}3!}$

Answer 1

Answer: (B)

$\frac{52!}{(17!{)}^{3}3!}$

The number of ways in which $52$52 cards can be divided into 44 sets, three of them having $17$17 cards each and the fourth one having just one card If 4n different things are to be equally distributed amongst 4 persons the numbers of ways are $4n! /(n!)^4$but if 4n things are to form 4 equal groups then the

numbers of ways are.

$P\left(E\right)=\frac{4n!}{n{!}^4\ast 4!}$

therefore,

Number of ways to form 4 sets, three of them having 17

Cards each and fourth just 1 card.

$P\left(E\right)=\frac{52!}{17{!}^3\ast 3!}$