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# Four cards are successively drawn with out replacement from a deck of 52 playing cards.What is the probability that all the four cards are kings?

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• In a pack of 52 cards there are 4 Kings
• If 4 cards are drawn is that replacement
• A defined as all 4 cards are Kings
• $K_I$ =getting King in( i)drawn
• AS ($k_1$$\cap$$K_2$$\cap$$K_3$$\cap$$K_4$$\cap$) are independent events
P($K_1$)=$\large\frac{4}{52}$
P($K_2$)=$\large\frac{3}{51}$
P($K_3$)=$\large\frac{2}{50}$
P($K_4$)=$\large\frac{1}{49}$
P(A)=$\large\frac{4}{52}\times$$\large\frac{3}{51}\times$$\large\frac{2}{50}\times$$\large\frac{1}{49}$
=$\large\frac{1}{270725}$

edited Jun 4, 2013