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....please upload a solution picture ||

Answer 1

Answer:

= $\frac{46}{7735}$

Step-by-step explanation:

Total number of possible hands = ⁵²C₇

i) Number of hands with 4 kings = ⁴C₄ × ⁴⁸C₃

(other 3 cards must be chosen from the rest 48 cards )

Hence, P ( a hand will have 4 Kings )

          = ⁴C₄ × ⁴⁸C₃ / ⁵²C₇ = $\frac{1}{7735}$

ii) Number of hands with 3 Kings and 4 non-Kings cards = ⁴C₃ × ⁴⁸C₄ / ⁵²C₇

       = $\frac{9}{1547}$

iii) P(atleast 3 Kings) = P(3 kings or 4 Kings)

        = P(3 Kings) + P(4 Kings)

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

GOOD LUCK !!