License Plate Combinations
Date: 11/26/2002 at 09:52:06 From: Eric Subject: Combinations How many different combinations of license plates are there for our state, given that we have 6 spaces that can be (0-9) numbers and (a-z) letters? I'm okay with one set of symbols, but with two sets of symbols what approach do I take? Thank you.
Date: 11/26/2002 at 11:39:14 From: Doctor Ian Subject: Re: Combinations Hi Eric, Try treating it as just one set of symbols, as if there were 36 digits instead of only 10. This isn't such a weird notion. For example, computer programmers often write numbers in base 16, also called 'hexadecimal'. Here's how you count in 'hex': 0 1 2 3 4 5 6 7 8 9 a b c d e f 10 11 12 13 14 15 16 17 18 19 1a 1b 1c 1d 1e 1f 20 21 22 ... So, if you have three spaces and you can use only numbers, there are 10 * 10 * 10 = 10^3 possible license plates. If you can use only letters, there are 26 * 26 * 26 = 26^3 possible license plates. If you can use either, there are (10+26)^3 = 36^3 possible license plates. Does this make sense? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
Date: 11/26/2002 at 12:48:52 From: Eric Subject: Thank you (Combinations) Yes, this helped out a great deal. Thanks again - you guys/gals are great.
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