Originally Posted by

**achacy** I have some difficulties in solving the following problem:

A deck of 52 playing cards, containing all 4 aces, is randomly divided into 4 piles of 13 cards each. Define events E1, E2, E3, E4 as follows:

E1 = {the first pile has exactly 1 ace},

E2 = {the second pile has exactly 1 ace},

E3 = {the third pile has exactly 1 ace},

E4 = {the fourth pile has exactly 1 ace},

Use the formula

$\displaystyle P(E_{1}\cap E_{2}...E_{4})=P(E_{1})P(E_{2}\mid E_{1})P(E_{3}\mid E_{1}E_{2})P(E_{4}\mid E_{1}E_2E_3) $

to find

$\displaystyle P(E_{1}\cap E_{2}\cap E_{3}\cap E_{4})$

the probability that each pile has an ace.