Math help, please

Factual Questions
21

I am suprised no one picked up on the repeated mistake that has been made.

26x26x26x10x10x10 is a wrong answer.

Years ago that would have been correct. Problem was every coupla years new plates had to be issued because they would run out of new plates. The correct answer to the OP question of how many possable is
10x26x26x26x10x10x10= 175,760,000.
It is digit (10),letterx3,numberx3.

Now one major corrective factor No plate will start with 0. Also 0 and o combinations are advoided, along with no no words and a few other.

Fun story
In 1964 Jonson was running for reelection and California was issuing new plates. some one mailed his new plates to white House. The plate was LBJ464

22

The OP specified to ignore the leading digit.

23

If you approach the problem from the other direction I find it to be simpler. The number of ways to pick 3 letters with at least one duplicate is the the number of ways to pick 3 letters minus the number of ways to pick 3 distinct letters. The same follows for the 3 digits, and you can multiply the two to get the total ways to make a plate with at least one duplicate in each.

Edit: I say duplicate a lot but I should really have said at least one repeated letter. (It also includes 3 of the same letter) I believe this satisfies your conditions.

I put this in code with tabs so it is hopefully easier to read:


Ways to pick 3 letters a-z:			26 x 26 x 26 	= 17,576
Ways to pick 3 numbers 0-9:			10 x 10 x 10 	= 1,000
Ways to make a plate combining the two:		17,576 x 1,000 	= 17,576,000

Ways to pick 3 distinct letters a-z:		26 x 25 x 24 	= 15,600
Ways to pick 3 distinct numbers 0-9:		10 x 9 x 8	= 720

Ways to make a plate with dupicate letters:	17,576-15,600 	= 1,976
Ways to make a plate with duplicate numbers:	1,000 - 720 	= 280

Ways to make a plate with duplicate numbers 
and duplicate letters:				1,976 x 280	= 553,280

Odds of getting a plate 
with duplicate letters and numbers:		553,280 / 17,576,000 
					= ~3.1479289940828402366863905325444%
24

Can’t edit my message any more but just imagine that wherever it says distinct in the code section it really says repeated.

25

Sorry I meant to say wherever it says duplicated in the code section it should say repeated.

:smack:

26

Why did the state of California issue a new plate to a Texas resident? Or am I missing some fact about LBJ? And technically he was not running for re-election as he was not elected president in 60 but became president when Kennedy died.

27

Okay, nice to see a sanity since my revised formula matches your answer with the same initial assumptions.

Any chance brujaja can come back and verify which set of assumptions, if either, is correct?

28

I read that as some resident of California obtaining his own California plates reading LBJ464, and then that California resident mailed those plates to the President.

29

Hi, all. Sorry for the delay; my roommate has become very ill, and the household is in kind of an ongoing uproar.

Personally, I don’t differentiate between AAB, ABA, and BAA. They’re all double letters to me, as far as license plates go. See, I ride my bike around a lot. And being, like many Dopers, a little OCD-having, I do things like read license plates as I ride.

Okay, yes, sometimes I add up the numbers, too. Yes, I know it’s pointless. I tell myself it’s a numerological oracle.

Anyway, what I’ve noticed is that it seems like there are an awful lot of plates with both a double letter and a double number. These are otherwise ordinary, I’m assuming non-vanity plates. It seems like a disproportionate number of them actually. Even if you take into account the fact that we are on series “6”, which multiplies the probability by seven in a perfect world where all cars remain on the road, that only makes roughly eleven point five percent of plates with double doubles. (considerably less, in reality.) What I’m seeing is more like double that.

But perhaps there is some kind of distribution scheme that skews these numbers seriously.

At first, I was going to take down the double-digit combinations that I observed each day (just the letter/number in question), assign each combination a unique color, and see what kind of design I came up with on graph paper. Who knows, maybe a message from the Ineffable, or the FSM. But I couldn’t come up with a color-assignment scheme that was logical and came out even. Plus I’d need, I don’t know, a whole lot more than sixty-four colors. 17,576,000 colors to be exact. Then I thought maybe if each letter had a color, and each number had a color, the grids could be two-part, like dominos, representing the letter color on top and the number color on the bottom.

Then I thought maybe I was pretty weird, got distracted, and wandered off to do something else.

Can you have OCD and ADHD at the same time?

30

The state did not, the guy who recieved the plate mailed it to the white house.

31

Whoops. Not seventeen million colors. But more than sixty-four.

Errrr… 263,640 colors. If I disregard the series number. Give or take a few. Your sums may vary.

32

I don’t see why not. They’re neurological disorders, not names for personality traits. Of course, I don’t see how that could be applicable to anything you mentioned. Suggestibility towards communication with unseen intelligences isn’t connected with obsessive-compulsive disorder or hyperactivity, but with less hip disorders like schizophrenia.

(Hint: You can reduce a color to a three-component vector by its RGB decomposition. Either map the letter-number pairs to red, green and blue by (A,0) |–> 0 , . . . , (Z,9) |–> 359, or take the three letter string componentwise to a color, CYK |–> (3,25,11) and use the numbers to map to a location on your graph however you deem best.)

33

California used to send out plates in batches to its DMV field offices. As a result, in your community, you would see a whole bunch of license plates with the same three-letter combination. For example, my parents owned a '72 Valiant with the license plate 417 AYT. There were a large number of AYT plates in our town. Similarly, I recall that there were certain combinations in my hometown when they started the 1XXX 111 number scheme.

If California is still using the local DMV offices to distribute plates, then that may still be happening. If so, if you happen to be in a place where an abnormal number of “double-letter” plates were issued, you might well notice that fact.

Some states have stopped issuing on-the-spot plates through the field offices and instead issue them from a central location, reducing or eliminating the need to have assigned batches. Not sure if California has done that or not.