The number of four digit numbers strictly greater than 4321 formed using the digits 0,1,2,3,4,5 with repetition of digit is

Step-by-step solution

The total number of four-digit numbers that can be formed using the digits 0, 1, 2, 3, 4, 5 with repetition is 5 6 6 6 = 1080 . We count the numbers less than or equal to 4321 . Case 1: Numbers starting with 0 are not four-digit numbers. So, the first digit can be 1, 2, 3, 4, 5 . Case 2: Numbers starting with 1, 2, 3 : First digit can be 1, 2, 3 ( 3 choices). The remaining three positions can be filled in 6 6 6 = 216 ways. Total = 3 216 = 648 . Case 3: Numbers starting with 4 : Subcase 3.1: Numbers starting with 40