Question 1144816: A student number system for a county requires that the student number be 5 characters. The first 3 characters are any single digit number, but no number can repeat and the last 2 characters must be letters, but no letter can repeat. How many unique student numbers are possible?
A. 1,370
B. 131,040
C. 250,000
D. 468,000
Is D correct?
The question and the answer choices in the link here: https://prnt.sc/p3ubbd
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
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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