Question

How many three-digit integers less than 801 have exactly two different digits in their representation ???

Answer 1

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Number of 3-digit integers that have exactly two different digits = Total number of 3 digit integers Number of 3 digit integers with 0 different digits (All digits are same) Number of 3 digit integers with 3 different digits (All digits are different)

Total number of 3 digit integers = 999-100+1 = 900

Number of 3 digit integers with 0 different digits (All digits are same) = 9*1*1 = 9

Number of 3 digit integers with 3 different digits (All digits are different) = 9*9*8 = 648

So, Number of 3-digit integers that have exactly two different digits = 900-9-648 = 243