The number of four digit natural numbers which contains exactly two distinct digits, is (A) 567 (B) 576 (C) 657 (D) 675

Explanation

The first (non-zero) digit of the number `F` (thousands digit) can be any one of nine.

The second digit `S` which is used if there are two digits can be any one of the nine digits different from the first.


Now consider the Hundreds Tens and Units digits in the case that there are two digits used in the number.

We have two possibilities `F` or `S` to fill each place but we exclude `FFF` as not involving two digits, so there are `2^3-1=7`
possible patterns with exactly two different digits and `9**9` ways of choosing the pair of digits in the first place.


Then there are `9` possibilities with just one digit.


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