In the first set, 17 cards out of 52 can be put in 52C17 ways. In the second set, 17 cards out of the remaining can be put in 35C17 ways. In the third set, 17 cards out of the remaining 18 in 18C17 ways.
In the last set, 1 card can be put only in 1 way.
Total number of ways in which 52 cards can be divided such that first 3 sets contain 17 cards and fourth set only one card is
52!/35!17! x 35!/18!17! x 18!/17!1! x 1 = 52!/(17!)3
The first three sets containing 17 cards each can be interchanged among themselves in 3! ways.
Therefore, total number of ways in the given problem is
