Answer
11,232,000
Work Step by Step
We have to find the number of license plates with 3 letters( distinct) followed by 3 digits (distinct). Since repetition is not allowed, we need to write down a 3-permutation of the set of 26 letters and follow it
by a 3-permutation of the set of 10 digits.
By the product rule, number of such plates =
$$(^{26}P_3)(^{10}P_3) =26. 25. 24. 10. 9. 8 = 11,232,000.$$
