Question

Four cards are successively drawn without replacement from a deck of 52 playing cards. What is the probability that all the four cards are king?

Answer 1

Let $E_1,E_2,E_3$ and $E_4$ are the events that the first, second, third and fourth card isking,respectively.
$:P(E_1\cap E_2\cap E_3\cap E_4)=P\left(E_1\right)\cdot P\left(E_2/E_1\right)\cdot P(E_3/E_1\cap E_2)\cdot P[E_4/(E_1\cap E_2\cap E_3\cap E_4]$
$=\frac{4}{52}\cdot \frac{3}{51}\cdot \frac{2}{50}\cdot \frac{1}{49}=\frac{24}{52\cdot 51\cdot 50\cdot 49}$
$=\frac{1}{13\cdot 17\cdot 25\cdot 49}=\frac{1}{270725}$