Answer
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Work Step by Step
The generalized pigeonhole principle applies here. The pigeons are the students, and the pigeonholes are the states, 50 in number.
By the generalized pigeonhole principle if we want at least 100 pigeons in at least one of the pigeonholes, then we need to have a total of N pigeons such that $\left \lceil{\frac{N}{50}}\right \rceil \geq 100$ i.e., N $\geq$ (99 . 50) + 1 = 4951. Therefore we need at least 4951 students to guarantee that at least 100 come from a single state.
