How many numbers are there between 100 and 1000 such that at least one of their digits is 7 ?How many numbers are there between 100 and 1000 which have exactly one of their digits as 7? pls explain the meaning of least and exactly.

The first digit of a number x from this range can be any of nine digits (1-9). The second two places can be filled by any of ten digits (0-9).

Therefore the probablility that only the first digit is a 7 is 1/9 x 9/10 x 9/10 = 81/900.

The probability that only the second digit is a 7:

8/9 x 1/10 x 9/10 = 72/900

The probability that only the third digit is a 7:

8/9 x 9/10 x 1/10 = 72/900

Adding the three mutually exclusive probabilities gives an overall proportion of 225/900, so with 900 numbers in the range there must be 225 with the digit 7 occurring only once.