What is sum of all rearrangements of the 4-digit number 3321?

Answer Choices

Correct answer marked below

27,777

28,888

29,997

Correct

29,999

39,999

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Explanation

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Official Explanation

Official

Total possible arrangements

=\frac{4!}{2!} = 12

[As 2-digits are similar]

Probability of 3 appearing at any position is two times as compared to that of 1 and 2. Hence 3 will appear 6 times and 1 and 2 will appear 3 times at each position.…

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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.