Question

How many four-digit numbers are there whose decimal notation contains not more than two distinct digits?

Answer 1

The first digit of the no$:$ $F$ can be any one of $9.$

The $2^{nd}$ digit $S$ which is need if there are $2$ digit can be any one of the $9$ digit from the first$.$

The hundreds tens end the unit digit in the case that there are two digit card in the no$:$

so two possibilities $F$ or $S$ to fill each place$.$

We exclude $FFF$ as not involving two digits$.$

$\therefore$ $2^3-1=7$ possible pattern in $9\times 9$ ways

$\therefore$ Total $=9\times 9\times 7+9=576$