The number of ways of making $s$ selections from among $r$ distinguishable possibilities, where the order does not matter and repetitions are allowed is $$\binom. This is a problem of "combinations with repetitions", also known as the "stars and bars problem". Try your best to clear all bricks and get higher scores Over hundreds of challengeable levels, clear the stages by eliminating bricks on the board. So you want to make $N-K$ selections from among $K$ boxes order does not matter repetitions are allowed. Balls Bricks Breaker is a simple addictive and pleasurable bricks breaker game Use your brain and swipe the balls to break all the bricks. The first combination corresponds to selecting box number $2$ twice the second to selecting box number $1$ twice and the third to selecting box $1$ once and box $2$ once. For your examples, having distributed one ball each in the two boxes, we are left with the problem of placing two balls in two boxes. Turns out that it's easier then to simply select the boxes that will have the balls. The problem now turns into the problem of counting in how many ways can you distribute $N-K$ indistinguishable balls into $K$ distinguishable boxes, with no constraints. Well, since each box has to contain at least one ball, place one ball in each box, leaving you with $N-K$ balls to distribute. From your examples, the boxes are distinguishable but the balls are not.
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