The number of five-digit numbers that contain 7 exactly once is

Step-by-step solution

We have, 0 ,   1 ,   2 ,   3 ,   4 ,   5 ,   6 ,   7 ,   8 ,   9 If 7 is used at first place then, then remaining four places, 5 digit total number made by remaining letters with repetition is 9 4 . Now, if 7 is placed any other four places, the total number 5 digit numbers made by remaining digits with repetition 4 × 8 × 9 3 . ∵   0 is not placed at the first place. Now, the total 5 -digit numbers = 9 4 + 4 × 8 × 9 3 = 9 3 9 + 32 = 41 9 3