GATE 2010 CS (CS1) – Question 10

General Aptitude · Quantitative Aptitude: Data Interpretation, Arithmetic and Number Computation · 2 marks · Multiple choice

Using the available digits 2,2,3,3,3,4,4,4,4 without exceeding their multiplicities, how many distinct four-digit numbers greater than 3000 can be formed?

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Correct answer: (B) 51

Explanation

The first digit must be three or four. Starting with three leaves three positions over {2,3,4}; of 27 strings, 222 and 333 exceed the remaining multiplicities, giving twenty-five. Starting with four leaves twenty-seven suffixes except 222, giving twenty-six. Total 25+26=51, B.

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