The number of arrangements of the numbers strictly between 10 and 1000 formed with the digits 0, 1, 2, 3, 4, 5, 6 without repetition is

Step-by-step solution

The numbers between 10 and 1000 consist of 2 -digit and 3 -digit numbers, strictly greater than 10 . Available digits: 0, 1, 2, 3, 4, 5, 6 (a total of 7 digits). For 2 -digit numbers: The tens place can be filled in 6 ways (excluding 0 ). The units place can be filled in 6 ways (any of the remaining 6 digits, including 0 ). Total 2 -digit numbers formed = 6 6 = 36 . Since the numbers must be strictly between 10 and 1000 , the number 10 itself must be excluded. Valid 2 -digit numbers = 36 - 1 = 35 . For 3 -digit num