The number of ways of dividing 52 cards amongst four players so that three players have 17 cards each and the fourth players just one card, is

For the first player, distribute the cards in  52C17, ways. Now, out of 35 cards left 17 cards can be put for second player in 35C17, ways. Similarly, for third player put them in  18C17, ways. One card for the last player can be put in  1C1, way. Therefore, the required number of ways for the proper distribution =52C17×35C17×18C17×1C1=52!35!17!×35!18!17!×18!17!1!×1!=52!(17!)3