A probability problem by Tanishq Varshney
Find the number of ways in which 4 different colored balls can be placed in four boxes whose colors are same of that of balls so that at least 2 balls go into the same colored boxes. Each box can only contain 1 ball.
The answer is 7.
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1 solution
First, we assume the four different colored balls as C, M, Y, K and so the boxes. Then, we have to consider the following situations, (C & M) in their respective colored boxes and Y in K while K in Y. In this way, for (C&Y), (C&K), (M&Y), (M&K), (Y&K) we get total 6 options for keeping 2 balls in their respective colored boxes. Then, if we try to put 3 balls in their respective colored boxes, the other one will also be in its own colored box. So, in fact, we are left with only one more option and that is (C, M, Y, and K) all the balls in their respective colored boxes. After all, the total number of ways becomes 7 in which at least 2 balls go into the same colored boxes. So, the answer is 7.