Find the probability that when a hand of 7 cards is drawn from a well shuffled deck of 52 cards, it contains (i) All king, (ii) 3 kings (iii) at least 3 kings.

Question

Find the probability that when a hand of 7 cards
is drawn from a well shuffled deck of 52 cards, it contains (i) All
king, (ii) 3 kings (iii) at least 3 kings

Ayush Jha · Accepted Answer

(i) the required probability is

$= \frac{4_{c_{4}} (48_{c_{3}})}{52_{c_{7}}} = \frac{1}{7735}$

(ii) the required probability is

$= \frac{4_{c_{3}} (48_{c_{4}})}{52_{c_{7}}} = \frac{9}{1547}$

(iii)the required probability is

$= \frac{4_{c_{4}} (48_{c_{3}}) + 4_{c_{3}} (48_{c_{4}})}{52_{c_{7}}} = \frac{46}{7735}$