GATE EC 2017 Set 2 — Question 64
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General Aptitude → Quantitative Aptitude → Permutations & Combinations
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Question
The number of 3-digit numbers such that the digit 1 is never to the immediate right of 2 is
Correct answer
(C) 881
Solution
To find the number of 3-digit numbers where the digit 1 is never to the immediate right of 2, we first calculate the total number of 3-digit numbers and then subtract those that contain the forbidden sequence '21'.
1.Total 3-digit numbers: The numbers range from 100 to 999. Total count = .
2.Forbidden numbers (containing '21'):
- Case 1: '21' in the first two positions (): The numbers are . There are 10 such numbers.
- Case 2: '21' in the last two positions (): The numbers are . There are 9 such numbers.
4.Total forbidden numbers: .
5.Allowed numbers: .
Therefore, the correct option is (C).Continue learning with Success Tracker
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