Number of ways of dividing 52 cards amongst four players equally, are

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6.Permutation and Combination

easy

The number of ways of dividing $52$ cards amongst four players equally, are

$\frac{{52\;!}}{{{{(13\;!)}^4}}}$

$\frac{{52\;!}}{{{{(13\;!)}^2}\;4\;!}}$

$\frac{{52\;!}}{{{{(12\;!)}^4}\;(4\;!)}}$

None of these

(IIT-1979)

Solution

(a) Required number of ways

${ = ^{52}}{C_{13}}{ \times ^{39}}{C_{13}}{ \times ^{26}}{C_{13}}{ \times ^{13}}{C_{13}}$

$ = \frac{{52\;!}}{{39\;!\; \times 13\;!}} \times \frac{{39\;!}}{{26\,!\; \times 13\;!}} \times \frac{{26\;!}}{{13\;!\; \times 13\;!}} \times \frac{{13\;!}}{{13\;!}} = \frac{{52\;!}}{{{{(13\;!)}^4}}}$.

Standard 11

Mathematics

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The number of ways of dividing $52$ cards amongst four players equally, are

Solution

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Determine $n$ if

$^{2 n} C_{3}:\,^{n} C_{3}=12: 1$