Find the number of ways in which a pack of 52 playing cards can be divided equally among four persons sitting around a circular table.

  • Option 1)

    \frac{52!\times 3!}{4!\times \left ( 13! \right )^{4}}

  • Option 2)

    \frac{52!}{4! \times\left ( 13! \right )^{4}}

  • Option 3)

    \frac{52!}{\left ( 13! \right )^{4}}

  • Option 4)

    \frac{52!\times3!}{\left ( 13! \right )^{4}}

 

Answers (1)

As learnt in concept

Groups of Unequal size -

Number of ways in which (m + n + p) things can be divided into unequal groups containing m, n and p things is 

 

 

- wherein

^{m+n+p}c_{m}. ^{n+p}c_{n}. ^{p}c_{p}=\frac{(m+n+p)!}{m\ !n!\ p!}

 

 Number of ways = \frac{52!}{(13!)^{4}}

 


Option 1)

\frac{52!\times 3!}{4!\times \left ( 13! \right )^{4}}

Incorrect option

Option 2)

\frac{52!}{4! \times\left ( 13! \right )^{4}}

Incorrect option

Option 3)

\frac{52!}{\left ( 13! \right )^{4}}

correct option

Option 4)

\frac{52!\times3!}{\left ( 13! \right )^{4}}

Incorrect option

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