## askme12345 3 years ago How many different ways can a nine digit number be written?

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

2. RagingSquirrel

Too many to count would be my best guess.

3. snappyjones

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

4. Hero

Order doesn't matter and there's repetition

5. RagingSquirrel

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

6. pokemon23

grrr

7. Hero

That doesn't really help

8. Diana

9! so it would be 9x8x7x6x5x4x3x2x1=362880

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

10. Diana

no it shouldnt

11. Hero

Zarkon...any input at all??

12. 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

13. Hero

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

14. Zarkon

$\frac{9!}{5!4!}$

15. Ishaan94

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

16. Zarkon

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

17. Zarkon

multinomial coefficients

18. Ishaan94

what is exactly meant by order doesn't matter?

19. Ishaan94

is 12 = 21 if order doesn't matter?

20. Zarkon

yes

21. Ishaan94

how would you do it for 121212121 if order matters

22. 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.

23. pokemon23

doesn't involve nPr or nCr?

24. Ishaan94

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

25. Ishaan94

I am bad at combinatorics :-/