seven 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?
Choose one: A) 60 B) 90 C) 240 D) 150 E) 180
Since the balls are all of different colors, let's permute them and then decide how many balls we put in each box.   For example, arrange in a row the balls, then decide: two balls go into the first box, next two in the second box, and the last ball goes to the third box.   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 150 + 90= 
<gadget id="calculator">150 + 90</gadget>
<output>240</output>
240 possibilities.   Answer 240.
<result>C</result>
seven 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?