Find the probability that when a hand of $7$ cards is drawn from a well shuffled deck of $52$ cards, it contains all Kings.
Find the probability that when a hand of $7$ cards is drawn from a well shuffled deck of $52$ cards, it contains all Kings.
Solution Total number of possible hands $=^{52} C _{7}$
Number of hands with $4$ Kings $=^{4} C _{4} \times^{48} C _{3}$ (other $3$ cards must be chosen from the rest $48$ cards)
Hence $P ($ a hand will have $4$ Kings $)$ $=\frac{^{4} C _{4} \times^{48} C _{3}}{^{52} C _{7}}=\frac{1}{7735}$
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