Question

In Shuffling a pack of cards$,$ four are accidentally dropped$;$ find the chance that the missing cards should be one from each suit.

Answer 1

Number of ways of choosing four cards $=$ ${}^{52}{C}_4$

Now we have to choose one card of each suit

Number of ways of choosing a card from each suit $=$ ${}^{13}{C}_1{\times }^{13}{C}_1{\times }^{13}{C}_1{\times }^{13}{C}_1$

$\therefore$ required probability $=\frac{{}^{13}{C}_1{\times }^{13}{C}_1{\times }^{13}{C}_1{\times }^{13}{C}_1}{{}^{52}{C}_4}=\frac{{\left(13\right)}^4}{{}^{52}{C}_4}$