Question

In a hand at whist find the chance that a specified player holds both the king and queen of trumps.

Note:Whist is a game of cards in which a standard pack of 52 cards is used.The game is played in pairs.In each round, a suit is randomly selected as 'Trump', which gets a preference over other suits for that particular round.

Answer 1

Total no. of ways${=}^{52}{C}_{13}$
One king and one queen of trump card,i.e., $11$ cards will be delivered to him from remaining $50$ cards${\Rightarrow }^{50}{C}_{11}$
Required probability$=\frac{{}^{50}{C}_{11}}{{}^{52}{C}_{13}}$
$\Rightarrow \frac{50!}{39!11!}\times \frac{13!39!}{52!}$
$\Rightarrow \frac{13\times 12}{52\times 51}$
$=\frac{156}{2652}$