I have a bag with 5 pennies and 6 nickels. I draw coins out one at a time at random. What is the probability that after draws I have removed no more than 2 pennies from the bag?
The cases are where we draw 4 pennies and 0 nickels, and 1 nickel and 3 pennies. This leads to a probability of (6*5 + 18*10)/C(11,4) = 7/11.