A) \[\frac{52\ !}{{{(17\ !)}^{3}}}\]
B) \[52\ !\]
C) \[\frac{52\ !}{17\ !}\]
D) None of these
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 \[=\frac{52\,!}{35\,!\,17\,!}\times \frac{35\,!}{18\,!\,17\,!}\times \frac{18\,!}{17\,!\,1\,!}\times 1\,!=\frac{52\,!}{{{(17\,!)}^{3}}}\].
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