In how many ways can a pack of 52 cards be (i) divided equally among four players in order (ii) divided into four groups of 13 cards each (iii) divided in 4 sets, three of them having 17 cards each and the fourth just one card?: Permutations and Combinations (Mathematics)

(i) The number of ways in which 52 cards be divided equally among four players in order

={ }^{52} C_{13} \times{ }^{39} C_{13} \times{ }^{26} C_{13} \times{ }^{13} C_{13}=\frac{{52}}{({13})^4}

(ii) The number of ways in which a pack of 52 cards can be divide equally into four groups of 13 cards each

\frac{1}{[4}{ }^{52} \mathrm{C}_{13} \times{ }^{39} \mathrm{C}_{13} \times{ }^{26} \mathrm{C}_{13} \times{ }^{13} \mathrm{C}_{13}=\frac{52}{\left[4(13)^4\right.}

(iii) The number of ways in which a pack of 52 cards be divided into four sets, three of them having 17 cards each and fourth just one card

=\frac{1}{[3} \times{ }^{52} C_{17} \times{ }^{35} C_{17} \times{ }^{18} C_{17} \times{ }^1 C_1=\frac{{52}}{{3(17)^3}}

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