The number of integers greater than 2000 that can be formed with the digits 0, 1, 2, 3, 4, 5, using each digit

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

Accepted Answer

1440. 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 C