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There are n street lights in a line. In order to conserve energy, the city decides...

There are n street lights in a line. In order to conserve energy, the city decides to turn off m of them.

a) Show that if n < 2m-1, there must be two neighboring lights that are turned off at the same time.

b) Assume that n >= 2m-1 and the m lights are chosen randomly. What is the probability that there are two neighboring street lights turned off at the same time?

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