GATE EE 2020 Set 1 — Question 8
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General Aptitude → Quantitative Aptitude → Permutations & Combinations
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Question
In four-digit integer numbers from 1001 to 9999, the digit group “37” (in the same sequence) appears ——— times.
Correct answer
(C) 280
Solution
We need to count the total number of times the sequence "37" appears in four-digit numbers from 1001 to 9999.
Let the four-digit number be .
The group "37" can appear in three possible positions:
Note: In numbers like 3737, the group "37" appears twice. In our calculation, 3737 is counted once in Position 1 and once in Position 3, correctly contributing 2 to the total count of appearances.
Let the four-digit number be .
The group "37" can appear in three possible positions:
1.Position 1 (): The first two digits are 37. There are such numbers (3700 to 3799).
2.Position 2 (): The middle two digits are 37. can be any digit from 1 to 9 (9 choices), and can be any digit from 0 to 9 (10 choices). Total = occurrences.
3.Position 3 (): The last two digits are 37. can be 1 to 9 (9 choices), and can be 0 to 9 (10 choices). Total = occurrences.
Total occurrences = .Note: In numbers like 3737, the group "37" appears twice. In our calculation, 3737 is counted once in Position 1 and once in Position 3, correctly contributing 2 to the total count of appearances.
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