The number of ways of dividing 52 cards among | vedclass

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Question

(a) For the first set number of ways $^{52}{C_{17}}$.

Now out of $35$ cards left $17$ cards can be put for second in $^{35}{C_{17}}$ ways similarly

Vedclass · Accepted Answer

$\frac{{52\;!}}{{{{(17\;!)}^3}}}$

Vedclass · Answer

(a) For the first set number of ways $^{52}{C_{17}}$.

Now out of $35$ cards left $17$ cards can be put for second in $^{35}{C_{17}}$ ways similarly for $3$ rd in $^{18}{C_{17}}$.

One card for the last set can be put in only one way.

Therefore the required number of ways for the proper distribution

$ = \frac{{52\,!}}{{35\,!\,17\,!}} 	imes \frac{{35\,!}}{{18\,!\,17\,!}} 	imes \frac{{18\,!}}{{17\,!\,1\,!}} 	imes 1\,! = \frac{{52\,!}}{{{{(17\,!)}^3}}}$.

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

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