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6.Permutation and Combination
easy
$52$ પત્તાને ચાર બાળકોમાં સમાન સંખ્યામાં કેટલી રીતે વહેચી શકાય.
A
$\frac{{52\;!}}{{{{(13\;!)}^4}}}$
B
$\frac{{52\;!}}{{{{(13\;!)}^2}\;4\;!}}$
C
$\frac{{52\;!}}{{{{(12\;!)}^4}\;(4\;!)}}$
D
એકપણ નહિ.
(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
