New 100$ bill with eight different digits - Not Ladder - How many combinations there are?

New 100$ bill with eight different digits - Not Ladder

The arrangement of the numbers is not important at all - the main thing that will be in the 100$ bill eight different digits

I wonder if some statistics major can tell us just how many combinations there are?
New 100$ Bill with 8 different digits :

 

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On eBay these are known as a "mixed ladder" serial number. They are not really recognized as a fancy type by most collectors. They're not worth much, but to the right collector there might be a small premium that they are willing to pay.

 

Many thanks


Interestingly statistically
how many combinations there are?

 

8x7x6x5x4x3x2x1= (Your answer) for each block they make

 

I believe it's higher, because we have 10 possible digits: 10x9x8x7x6x5x4x3 for any given block. There area a lot of these notes out there.

 

True, completely forgot about 0

 

If your going for 8 completely different digits with no repetition the possible combinations assuming 10 numbers, 8 chosen with no repetition is only 45

n!
(n-r)! (r!)

10!
(10-8)! (8!)

10!
2! (8!)

10x9x8!
2! (8!)

10x9
2!

90
2x1

90/2= 45 combinations

 

I LOVE this forum!

 

You did a combination calculation. We are looking for permutations, because order matters. With a combination, 12345678 is indistinguishable from 85647213. So there are 45 separate combinations of 8 numbers if we don't consider the order. In our case, we have many more results, because a different order means a different note.

The correct formula is n! / (n-r)! = 10! / (10-8)! =

(10x9x8x7x6x5x4x3x2x1) / 2x1 =

10x9x8x7x6x5x4x3 =

1,814,400 notes per block. That is of course if we factor in high serial numbers that are presently reserved for sheets.

P.S. Thank you for the wonderful flashback to high school math.

 

I simply did what the original poster asked to be done which was calculate the possible combinations with arrangement not being important. But your correct if the order is important.

 

If you're enjoying this sort of thing, you might like this thread over on the Where's George forums, where we went entirely overboard calculating probabilities for all sorts of fancy (and not-so-fancy) serials....

 

I don't understand this fancy serial number thing. A fancy serial number is no more rare than a non-fancy. Isn't that true?

 

There are an equal number of notes printed for serial 0000 0001 and serial 8402 4536. Your odds of finding either serial are equal (strictly mathematically). If you were hunting for a specific number, your odds of finding it are no different from finding a serial number 1, assuming it hasnt been pulled by someone else. No given serial number is rarer than another, however certain number combinations (permutations) are desirable. There are millions of notes with arbitrary numbers, but they have no significance to collectors.

 

There are, just so you don't sit up nights shaking your head about it, plenty of paper money collectors that see it pretty much as you do, farmer. This numerology fanaticism can be a bit much. If a SN #1 showed up in my change, I'd certainly keep it, but I am amazed that so much of the US collecting population treats "fancy numbers" in such high regard.

 

Considering how much people spend on astrology, numerology and fortune telling, I'm not surprised by people's fascination with numbers. That's part of the allure. The other part of it is rarity. There are far fewer serial #1 notes available than there are most uncommon large size notes. And you can see how much those command.

If you found a serial #1, you damn well better keep it. You're giving up thousands of dollars if you release it into circulation.