Question 1144816
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We have 5 slots to fill. Let's call them A,B,C,D,E


The first three slots (A,B,C) are a single digit number. We have 10 choices for slot A, 9 for B, and 8 for C. So far we have 10*9*8 = 720 different ways to form a three digit number where the digits do not repeat. It's possible to select 0 first. 


For slot D, we have 26 letters to pick from. For slot E, we have 25 letters left over. So we have 26*25 = 650 different two letter combos (repeat not allowed)


Multiply the two sub-results and we end up with: 720*650 = 468,000


Choice D is the correct answer.


As shorthand you can simply multiply everything out as such
10*9*8*26*25 = 468,000
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