The number of 5 digited numbers that contain 7 exactly once is

7    If 7 is in first place then the no of arrangements=94 .                 ( 2nd, 3rd,4th,5th blanks can be filled in 9 ways each )                    If 7 is in any one of the remaining 4 places then no of arrangements =4×8×93                     (The first place can be filled  in 8 ways (except 0 and 7)   and the remaining 4 blanks can be filled in  4×93 ways)  The number of 5 digited numbers that contain 7 exactly once is = 94+ 8×4×93                                                                                                             =93(9+32)=41(93)