Answer:

Correct Answer: A

Solution:

• For the first set number of ways $ ^{52}C _{17} $ . Now out of 35 cards left 17 cards can be put for second in $ ^{35}C _{17} $ ways similarly for 3rd in $ ^{18}C _{17} $ . One card for the last set can be put in only one way. Therefore the required number of ways for the proper distribution $ =\frac{52!}{35!17!}\times \frac{35!}{18!17!}\times \frac{18!}{17!1!}\times 1!=\frac{52!}{{{(17!)}^{3}}} $ .