There are 50 balls. 40 Black and 10 White. You draw balls without replacement and win if you draw all 10 white balls before drawing 4 black balls in a row.
How do I calculate the probability of winning? What if only 9 or 8 white balls need to be drawn to win?
Hint: Draw all 50 balls regardless. Then there are $\binom{50}{10}$ ways to place the 10 white balls. In how many is each white ball preceded by a run of no more than 3 blacks?