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

Here, we have to divide 52 cards into 4 sets, three 

of them having 17 cards each and the fourth one having just 

one card. First we divide52 cards into two groups of 1 card and

51 cards. This can be done in $\frac{52!}{1!51!}$ ways

Now, every group of 51 cards can be divided into 3 groups of  17 each in $\frac{51!}{(17!{)}^{3}3!}$

Hence, the required number of ways

$=\frac{52!}{1!51!}\cdot \frac{51!}{(17!{)}^{3}3!}=\frac{52!}{(17!{)}^{3}3!}$