Question

In a hand at whist what is the chance that the $4$ kings are held by a specified player$?$

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

We know that there are $13$ cards to be delivered at hand
Total no. of ways${=}^{52}{C}_{13}$
$\because 4$ King held be specific player,
So $9$ remaining cards to be delivered to him from remaining $48$ cards
No. of ways favorable${=}^{48}{C}_9$
Required probability$=\frac{{}^{48}{C}_9}{{}^{52}{C}_{13}}$
$=\frac{48!}{9!39!}\times \frac{13!39!}{52!}$
$=\frac{11}{4165}$