Probability that when a hand of 7 cards is drawn from a well shuffled deck of 52 cards, it contains&

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14.Probability

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Find the probability that when a hand of $7$ cards is drawn from a well shuffled deck of $52$ cards, it contains $3$ Kings.

A

$\frac{9}{1547}$

B

$\frac{9}{1547}$

C

$\frac{9}{1547}$

D

$\frac{9}{1547}$

Solution

Total number of possible hands $=^{52} C _{7}$

Number of hands with $3$ Kings and $4$ non-King cards $=^{4} C _{3} \times^{48} C _{4}$

Therefore $P (3$ Kings $)=\frac{^{4} C _{3} \times^{48} C _{4}}{^{52} C _{7}}$ $=\frac{9}{1547}$

Standard 11

Mathematics

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