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- askme12345

How many different ways can a nine digit number be written?

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- askme12345

How many different ways can a nine digit number be written?

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- askme12345

For example : 121212121, order doesnt matter how many different ways can you arrange the digets?

- RagingSquirrel

Too many to count would be my best guess.

- anonymous

9 times 9 times 9 times 9 times 9 times 9 times 9 times 9 times 9 =
387 420 489

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- Hero

Order doesn't matter and there's repetition

- RagingSquirrel

There are 1,000,000,000 different 9-digit numbers, ranging from 000,000,000 to 999,999,999.

- pokemon23

grrr

- Hero

That doesn't really help

- Diana

9! so it would be 9x8x7x6x5x4x3x2x1=362880

- askme12345

since there is 4 2's and 5 1's wouldnt some overlap though?

- Diana

no it shouldnt

- Hero

Zarkon...any input at all??

- Zarkon

are you looking to find the number of arrangement of 121212121 or any 9 digit number. The first is trivial...the second is a much longer computation

- Hero

number of arrangement of 121212121. I don't remember how to do it.

- Zarkon

\[\frac{9!}{5!4!}\]

- anonymous

uh oh I did \[\frac{9!}{4!} + \frac{9!}{5!}\]

- Zarkon

if you wanted to arrange 112223333
\[\frac{9!}{2!3!4!}\]

- Zarkon

multinomial coefficients

- anonymous

what is exactly meant by order doesn't matter?

- anonymous

is 12 = 21 if order doesn't matter?

- Zarkon

yes

- anonymous

how would you do it for 121212121 if order matters

- Zarkon

so if you didn't care about the order of 12121212 you would treat all the \(\frac{9!}{5!4!}\) ways to arrange it as being the same.

- pokemon23

doesn't involve nPr or nCr?

- anonymous

hmm 5 1s and 4 2s total 9 position
is it \[\frac{9!}{4!} + \frac{9!}{5!}\]? (order matters)

- anonymous

I am bad at combinatorics :-/

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