AoPS Wiki:Problem of the Day/July 15, 2011

A stork lives by Lake Michigan. Every day, it goes out to the lake to catch fish. It always searches the same 10 spots every day. The probability that the stork will find a fish in that area on that day is $\frac{1}{2}$. It never finds more than one fish in the same spot on the same day. After the stork has searched all 10 spots, it returns to its nest to feed the fish to its babies. There are 6 baby storks that the adult stork feeds, and each one is satisfied with one fish. What is the probability that, on any single day, the stork will find enough fish to satisfy all of the baby storks?