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# There are Five balls of different colour and 3 boxes of different size. The balls are to be placed in the boxes so that no box is empty. In how many ways this can be done?

Balls in the boxes can be (2,2,1),(1,2,2),(2,1,2) ways
$=3.(^5C_2.^3C_2.^1C_1)=90\:ways$
or
$(1,1,3),(1,3,1),(3,1,1)$
$=3.(^5C_1.^4C_1.^3C_3)=60\:ways$
$\therefore$ The required no. of arrangements = $90+60=150$