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Find the number of ways in which 4 disti...

Find the number of ways in which 4 distinct balls can be put into 3 distinct boxes so that no remains empty

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To find the number of ways to distribute 4 distinct balls into 3 distinct boxes such that no box remains empty, we can use the principle of inclusion-exclusion. Here is a step-by-step solution: ### Step 1: Total Distributions Without Restrictions First, we calculate the total number of ways to distribute 4 distinct balls into 3 distinct boxes without any restrictions. Each ball can go into any of the 3 boxes, so the total number of distributions is: \[ 3^4 = 81 \] ...
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