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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?

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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 = $90+60=150$
answered Aug 31, 2013 by rvidyagovindarajan_1
 

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