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 atleast $3$ Kings.

A

$\frac{46}{7735}$

B

$\frac{46}{7735}$

C

$\frac{46}{7735}$

D

$\frac{46}{7735}$

Solution

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

$P ($ atleast $3$ King $)= P (3 $ Kings or $4$ Kings $) $

$= P (3$ Kings $)+ P (4 $ Kings $)$

$=\frac{9}{1547}+\frac{1}{7735}=\frac{46}{7735}$

Standard 11

Mathematics

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(IIT-2016)