Question

# You have to divide a pack of $$52$$ cards equally among $$4$$ players. In how many ways the cards can be divided in $$4$$ sets, $$3$$ of them having $$17$$ cards each & the $$4^{th}$$ with $$1$$ card

A
52!4!3!(17!)3
B
52!(3!)3(17!)
C
52!(3!)(17!)
D
52!(17!)3

Solution

## The correct option is A $$\displaystyle \frac{52!4!}{3!(17!)^3}$$First select $$17$$ cards out of $$52$$ cards in $$^{52}C_{17}$$. Then select $$17$$ from the remaining $$35$$ cards in $$^{35}C_{17}$$. Then select $$17$$ again from the remaining $$18$$ in $$^{18}C_{17}$$ ways. Total no. of ways $$=$$  $$^{52}C_{17} \times ^{35}C_{17} \times ^{18}C_{17} \times 1 \times ^4C_3$$$$=$$   $$\displaystyle \frac{52!4!}{3!(17!)^3}$$Maths

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