From a pack of 52 cards, 4 are drawn one by one without replaceme… - Vidyadip

Question

From a pack of 52 cards, 4 are drawn one by one without replacement. Find the probability that all are aces (or kings).

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Answer

A = First card Ace
B = Second card Ace
C = Third card Ace
D = Fourth card Ace
P (All four drawn are Ace, without replacement)
$=\text{P}(\text{A})\ \text{P}\Big(\frac{\text{B}}{\text{A}}\Big)\ \text{P}\Big(\frac{\text{C}}{\text{A}\cap\text{B}}\Big)\ \text{P}\Big(\frac{\text{D}}{\text{A}\cap\text{B}\cap\text{C}}\Big)$
$=\frac{4}{52}\times\frac{3}{51}\times\frac{2}{50}\times\frac{1}{49}$ [Since, there are four Ace in 52 cards]
$=\frac{1}{270725}$
Required Probabilty $=\frac{1}{270725}$

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