• question_answer The number of ways of dividing 52 cards amongst four players so that three players have 17 cards each and the fourth player just one card, is [IIT 1979] A) $\frac{52\ !}{{{(17\ !)}^{3}}}$ B) $52\ !$ C) $\frac{52\ !}{17\ !}$ D) None of these

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  $=\frac{52\,!}{35\,!\,17\,!}\times \frac{35\,!}{18\,!\,17\,!}\times \frac{18\,!}{17\,!\,1\,!}\times 1\,!=\frac{52\,!}{{{(17\,!)}^{3}}}$.