CAT 2022 Slot 2 QA Question & Solution
Modern MathMedium
Question
The number of integers greater than 2000 that can be formed with the digits 0, 1, 2, 3, 4, 5, using each digit at most once, is
Options
1440
1200
1480
1420
Solution
Case 1: 4-digit numbers
Given digits - 0, 1, 2, 3, 4, 5
_, _, _, _
As the numbers should be greater than 2000, first digit can be 2, 3, 4 and 5.
For remaining digits, we need to arrange 3 digits from the remaining 5 digits, i.e. 5*4*3 = 60 ways
Total number of possible 4-digit numbers = 4*60 = 240
Case 2: 5-digit numbers
_, _, _, _, _
First digit cannot be zero.
Therefore, total number of cases = 5*5*4*3*2 = 600
Case 3: 6-digit numbers
_, _, _, _, _, _
First digit cannot be zero.
Therefore, total number of cases = 5*5*4*3*2*1 = 600
Total number of integers possible = 600 + 600 + 240 = 1440
The answer is option A.