Assume I want to find out how many combinations there are for a 8 digit word with 6 uppercase letters and 2 distinct numbers, e.g. A7BC9DEF, 1A0CRDEF, ...
how many combinations are there?
My approach's solution is : $26^6 \cdot 90 \cdot 8 \cdot 7$
90 because there are 90 possible numbers with two distinct digits, i.e. $01, 02, \ldots, 09, 10, 12, \ldots, 21, 23, \ldots, 98 \rightarrow 99 - 9$ valid numbers)
$8 \cdot 7$ because the digits of the 90 possible numbers can be found at $8 \cdot 7$ different indices.
I had combinatorics a long time ago in school so I thought asking here for clarification might be a good idea. Thanks in advance!