How many three-digit integers less than have exactly two different digits in their representation (for example, or
Answer:
- Let the two different digits be and
Therefore, the required integers are of the form or - If the repeated digits are zero, we must ignore the form as they will give us one and two digit numbers. etc.
So, if the integers have the form and can be
Therefore, there are integers with two zeros, - When the repeated digit is non-zero, the integers are of the form or
If can be or therefore there are possible integers but we must ignore as this is a two-digit integer.
Since your number is less than so we must ignore
This gives different integers.
Similarly, there will be an additional integers for every non-zero value of .
Therefore, the total number of three-digit integers less than that have exactly two different digits in their representation - Hence, there are three-digit integers less than that have exactly two different digits in their representation.