Emma has a bag that contains 6 nickels and 5 pennies. She draws coins from the bag at random, without replacement. What is the probability that after drawing 4 coins, she has removed at most 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.