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combinatorics ace mock

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Number of ways we can assign 5 persons into 3 different rooms, so that each room contains at least 1 person is _____________
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This is same as the number of onto functions from a set of 5 objects to a set of 3 objects.

Required number of ways = $3^{5}-\binom{3}{1}\left ( 3-1 \right )^{5}+\binom{3}{2}\left ( 3-2 \right )^{5}$ = 150

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