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 preference over other suits for that particular round.

• A. Hence required probility $p=\frac{11}{4165}$
• B. Hence required probility $p=\frac{22}{4165}$
• C. Hence required probility $p=\frac{11}{8330}$
• D. Hence required probility $p=\frac{33}{4165}$

Answer 1

The correct option is A Hence required probility $p=\frac{11}{4165}$

We know that 13 cards are delivered to a hand at whist .
Now, n=total no. of ways =${}^{52}{C}_{13}=\frac{52!}{13!39!}$
Since 4 kings are held by a specified player, 9 more cards are to be delivered to him from the remaining 48 cards
So, m= favourable no. of ways =${}^{48}{C}_9=\frac{48!}{9!39!}$
Hence required probility $p=\frac{m}{n}=\frac{48!}{9!39!}\times \frac{13!39!}{52!}$
$=\frac{\mathrm{13.12.11.10}}{\mathrm{52.51.50.49}}$
$=\frac{11}{4165}$