Statistics and Probability Problems

1) A sailing ship has three masts and twelve different signal flags. Any number of flags can be put on any number of the masts in any order (top to bottom). How many distinct signals can be sent with this set up? A signal is a configuration of flags....not all flags must be used.
2) A ten story building has ten elevators serving all floors. Assuming the elevators are uniformly distributed among the floors at any time, what is the probability that an elevator answering a call on the ninth floor comes from below. What about the second floor from above? Explain why this does not mean elevator cabs are being manufactured in the middle of the building and thrown off the roof or stored in the basement.
3) You buy two flood lights rated for 1000 hours (that is the mean lifetime). You turn them on and leave them on. What is the probability that they both burn out within one day of each other?

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