Lights on!

Discrete Mathematics Level pending

At 7pm, the 50 story building that Calvin works in has some floors which have the lights on and some floors which have the lights off. 50 people \(p_1, p_2, \ldots, p_{50}\) walk past the building, and person \(p_i\) looks at floors \(i, 2i, 3i, \ldots\) and records the number of floors he looked at that had the lights on as \(x_i\). Calvin calculates that \(\sum\limits_{i=1}^{50} x_i = 200\). If at least 47 floors had their lights on, determine the number of possible combinations of floors which had their lights on.

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