Question

In a hand at Whist, what is the probability that four kings are held by a specified player?

 

Answer 1

In a hand at whist, the specified players have 13 cards including fourkings.
Four kings can be drawn out of four in ⁴C₄ ways.
The remaining nine cards held by him can be drawn out of the remaining 48 cards in the pack in ⁴⁸C₉ ways.
The total number of ways in which four kings and nine other cards can be drawn is ⁴C₄× ⁴⁸C_9. 
Favourable number of cases = ⁴C₄× ⁴⁸C₉ 
Also, exhaustive number of cases = ⁵²C₁₃
∴ Required probability = \[\frac{ ^{4}{}{C}_4 \times ^{48}{}{C}_9}{^{52}{}{C}_{13}} = \frac{11}{4165}\]