How many different ways can we distribute 5 unique balls into 4 distinct boxes, given that any box can hold any number of balls?

Answer Choices

Correct answer marked below

256

625

1024

Correct

3125

243

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Explanation

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Official Explanation

Official

To determine the number of ways to distribute 5 unique balls into 4 distinct boxes, we can analyze the process step by step. Stage 1: Choose a box for the 1st ball. There are 4 boxes available, so there are 4 options for this stage. Stage 2: Choose a box for the 2nd ball. Again, there are 4 boxes, providing 4 choices. Stage 3: Choose a box for the 3rd…

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What this question tests

What it tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Common trap

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.