O Tommy
One day, Tommy went to school with 9 indistinguishable balls for his talent shows. But there's a strict rule he must follow to participate, he must share his 9 balls among his 3 classrooms(Calculus, Geometry, Combinatoric) after his performance. Each class must receive at least one ball. How many ways can he distribute his 9 balls?
The answer is 28.
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1 solution
This is a classic example of bars and stripes/balls and urns question. We represent 9 balls as 9 stars and two bars to create 3 spaces. For example, one configuration may look like l * l * We can make one class room or two classrooms have no balls l *l * So there are 11 slots we have to fill out. However Tommy must give one ball to each classroom so we are left with 6 balls after giving one to each classroom( 6 balls and *l *l *). Now all we have to do is find the way to distribute 6 balls and 2 bars into 8 slots which C(8,2) which is 28.