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How many different automobile license numbers can be formed by using $1$ to $6$ digits preceded by a letter if the digit immediately following the letter cannot be zero and the letters O and I are excluded?

My answer is $24\cdot9\cdot10\cdot10\cdot10\cdot10\cdot10 = 21600000$

Is this correct?

ArsenBerk
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Madisson
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  • This looks like it would be the right answer if every licence plate used exactly 6 digits. Do you need to consider licence plates that use fewer than 6 digits? – Paul Aljabar Dec 31 '17 at 18:11
  • I think i will use 6 digits because it is stated in the problem. I'm also confused because automobile license consist of 3 letters and 3 digits. Since it is indicated in the problem i used 6 digits. – Madisson Dec 31 '17 at 18:25
  • Well, I think you're correct if the question wants you to find the number of possibilities with exactly six digits. If plates are allowed any number of digits between 1 and 6 (inclusive), then you'd need to add together a number of similar terms. I don't think the question is meant to reflect what system is actually used for plates in the real world. – Paul Aljabar Dec 31 '17 at 18:29
  • I agree. Since the problem stated that it is 6 digits. Then is should probably follow it.Do you think my answer is correct? – Madisson Dec 31 '17 at 18:35
  • I think it is correct if the the plates must have exactly six digits. – Paul Aljabar Dec 31 '17 at 19:47

1 Answers1

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You have $24.9$ one digit plates, $24.9.10$ two digit plates, ..., and $24.9.10^5$ 6 digit plates. Adding those numbers results in a total of $24.(10^6-1)$ plates. That is $23,999,976$ plates all together.

Mohammad Riazi-Kermani
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