In a hand at Whist, what is the probability that four kings are held by a specified player?
In a hand at whist. the specified player has 13 cards including 4 kings. Four kings can be drawn out of 4 in 4C4 ways. The remaining 9 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 4 kings and 9 other cards can be drawn is 4C4×48C9
Number of favourable cases =4C4×48C9
Number of exhaustive cases = 52C13
∴ Required probability
=Number of favourable outcomesTotal number of possible outcomes
=4C4×48C952C13=114165