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There are four balls of different colour...

There are four balls of different colours and four boxes of colours, same as those of the balls. The number of ways in which the balls, one in each box, could be placed such thast a ball does not go to a box of its own colour is: (A) `|__4-1` (B) 9 (C) `|__3+1` (D) none of these

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To solve the problem of placing four balls of different colors into four boxes of the same colors such that no ball is placed in the box of its own color, we can use the concept of derangements. A derangement is a permutation of elements where none of the elements appear in their original position. ### Step-by-Step Solution: 1. **Understanding the Problem**: We have 4 balls (let's say colors A, B, C, D) and 4 boxes (also colored A, B, C, D). We need to find the number of ways to place the balls in the boxes such that no ball goes into the box of its own color. 2. **Using the Derangement Formula**: ...
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