Question

The numbers of ways in which a pack of 52 cards can be divided equally among four players in orders is

A
52!(13!)4
B
52!(13!)44!
C
52!13!
D
52!4!×13!

Solution

The correct option is B $$\dfrac { 52! }{ { \left( 13! \right) }^{ 4 }4! }$$If $$4n$$ different things are to be equally distributed amongst $$4$$ persons the numbers of ways are $$\dfrac{4n!} {(n!)^4}$$ but if $$4n$$ things are to form $$4$$ equal groups thenthe numbers of ways are $$\dfrac{4n!} {(n!)^4\times 4!}$$Number of ways of dividing $$52$$ cards equally among $$4$$ players $$=\dfrac{52!} {(13!)^4 \times 4!}$$Maths

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