The total number of ways, of dividing 52 cards amongst 4 players, so that 3 players have 17 cards each and fourth player has just one card, are

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Aicharya · Accepted Answer

Apply permutations and combinations to find the required number of ways
The first player can be dealt 17 cards out of the deck of 52 cards in \({ }^{52} C_{17}\) ways.
The second player can be dealt 17 cards out of the remaining 35 cards in \({ }^{35} C_{17}\) ways.
The third player can be dealt 17 cards out of the remaining 18 cards in \({ }^{18} C_{17}\) ways.
There is only one way of getting the last player one card.
Hence, the required number of ways \(=\frac{52 !}{35 ! 17 !} \times \frac{35 !}{18 ! 17 !} \times \frac{18 !}{17 ! 1 !} \times \frac{1}{3 !} \ldots .(3 !\) is included as none of those sets are distinct)
\(=\frac{52 !}{(17 !)^3 \times 3 !}\)

The total number of ways, of dividing 52 cards amongst 4 players, so that 3 players have 17 cards each and…

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