Numbers between 100 and 1000 are 3-digit numbers.

A 3-digit number is to be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, where exactly one of the digits is 7.

When 7 is in unit’s place:

Unit’s place digit is 7.

∴ it can be selected in 1 way only.

10’s place digit can be selected in 9 ways.

100’s place digit can be selected in 8 ways.

Total numbers which have 7 in unit’s place = 1 × 9 × 8 = 72.

When 7 is in 10’s place:

Unit’s place digit can be selected in 9 ways.

10’s place digit is 7.

∴ it can be selected in 1 way only. 100’s place digit can be selected in 8 ways.

∴ A total number of numbers which have 7 in 10’s place = 9 × 1 × 8 = 72.

When 7 is in 100’s place:

Unit’s place digit can be selected in 9 ways. 10’s place digit can be selected in 9 ways.

100’s place digit is 7.

∴ it can be selected in 1 way only.

∴ Total numbers which have 7 in 100’s place = 9 × 9 × 1 = 81.

∴ Total numbers between 100 and 1000

having digit 7 exactly once = 72 + 72 + 81 = 225