GATE 2017 EC (EC2) – Question 9

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

The number of three-digit numbers in which digit 1 is never immediately to the right of digit 2 is

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Correct answer: (C) 881

Explanation

There are 900 three-digit numbers, from 100 through 999. Exclude those containing the adjacent pattern 21.

If 21 occupies the hundreds and tens places, the units digit has ten choices, giving 210–219. If it occupies tens and units, the hundreds digit has nine choices, giving 121,221,…,921.

These cases cannot overlap in a three-digit number, so 19 numbers are excluded. The count is $900-19=$ **881, C**.

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