Answer
20,077,200.
Work Step by Step
Step 1- Find the number of ways to choose the letters.
By the sum -rule this is the sum of the number of ways to use two letters and the number of ways to use three letters.
By the product rule there are ${26^2}$ ways to choose two letters and $26^3$ ways to choose three letters. Therefore there are $26^2$ + $26^3$ ways to choose the letters.
Step 2-Similarly there are $10^2$ + $10^3$ ways to choose the digits.
(10 ways to choose a digit -0,1,...,9)
Thus the answer to the question is ($26^2 + 26^3 )(10^2 + 10^3$) = 18252 · 1100 = 20,077,200.
