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 = $\frac{{}^{4}C_4\times {}^{48}C_9}{{}^{52}C_{13}}=\frac{11}{4165}$