Question

The number of ways of dividing 52 cards amongst four players, so that three players have 17 cards each and the fourth player has just one card, is.

विकल्प

• `(52!)/(17!)^3xx4`

• 52!

• `(52!)/(17!)`

• None of these

Answer 1

`(52!)/(17!)^3xx4`
Explanation:

First of all select 17 cards out of 52 cards in `" ^52C_17` ways. Now, again select 17 cards out of remaining 35 cards in `" ^35C_17` ways. Similarly, for the third player select, 17 cards out of remaining  18 cards in `"^18C_17` ways and the fourth player can get last left card in 1 way.
Also, 3 players who get 17 cards each can be selected in `"^4C_3` i.e. 4 ways.

∴ The required number of ways for the proper distribution

= `"^52C_17xx^35C_17xx^18C_17xx^1C_1xx4`

= `(52!)/(35!17!)xx(35!)/(18!17!)xx(18!)/(17!1!)xx4=(52!)/(17!)^3xx4`