Five balls of different colors are to be placed in three different boxes such that any box contains at least 1 ball . What is the maximum number of different ways in which this can be done?
Options.
A) 60  B) 90  C) 120  D) 150  E) 180
Since in each box there must be at least one ball, we have the possibilities of (2,2,1), (2,1,2), (1,2,2) OR (3,1,1), (1,3,1), (1,1,3) balls in the three boxes.   For the 2,2,1 type arrangements, we have [5!/(2!2!1!)]*3 = 90 possibilities. Inside a box, it doesn't matter the order of the balls.   For the 3,1,1 type arrangements, we have [5!/(3!1!1!)]*3 = 60 possibilities.   Total of 90 + 60= 
<gadget id="calculator">90 + 60</gadget>
<output>150</output>
150 possibilities.   Answer 150.
<result>D</result>
Five balls of different colors are to be placed in three different boxes such that any box contains at least 1 ball . What is the maximum number of different ways in which this can be done?