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There are four large urns numbered 1 to 4. The number of different ways all the three balls numbered 1 to 3 can be kept inside the four urns is
Explanation
This is a problem of permutations involving the distribution of distinct objects into distinct containers. Since the balls are numbered (1 to 3) and the urns are numbered (1 to 4), both the objects and the containers are distinct.
- Ball 1 can be placed in any of the 4 urns (4 choices).
- Ball 2 can be placed in any of the 4 urns (4 choices).
- Ball 3 can be placed in any of the 4 urns (4 choices).
According to the Fundamental Principle of Counting (Multiplication Rule), the total number of ways is the product of the independent choices for each ball:
Total ways = 4 × 4 × 4 = 43 = 64
In general, the number of ways to distribute r distinct objects into n distinct bins (where each bin can hold any number of objects) is given by the formula nr. Here, n = 4 and r = 3, resulting in 64.