Question

# In how many ways can a pack of $$52$$ cards be divided in $$4$$ sets, three of them having $$17$$ cards each and fourth just $$1$$ card?

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

Solution

## The correct option is A $$\displaystyle\frac{52!}{3!(17!)^3}$$First we divide $$52$$ cards into two sets which contains $$1$$ and $$51$$ cards respectively is $$\quad\displaystyle\frac{52!}{1!\space 51!}$$Now $$51$$ cards can be divided equally in three sets each contains $$17$$ cards (Here order of sets is not important) in $$\displaystyle\frac{52!}{3!(17!)^3}$$ waysHence, the required number of ways $$\quad = \space \displaystyle\frac{52!}{1! \space 51!} \times \displaystyle\frac{51!}{3!\space(17!)^3}$$Maths

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