## askme12345 Group Title How many different ways can a nine digit number be written? 2 years ago 2 years ago

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

2. RagingSquirrel Group Title

Too many to count would be my best guess.

3. snappyjones Group Title

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

4. Hero Group Title

Order doesn't matter and there's repetition

5. RagingSquirrel Group Title

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

6. pokemon23 Group Title

grrr

7. Hero Group Title

That doesn't really help

8. Diana Group Title

9! so it would be 9x8x7x6x5x4x3x2x1=362880

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

10. Diana Group Title

no it shouldnt

11. Hero Group Title

Zarkon...any input at all??

12. Zarkon Group Title

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 Group Title

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

14. Zarkon Group Title

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

15. Ishaan94 Group Title

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

16. Zarkon Group Title

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

17. Zarkon Group Title

multinomial coefficients

18. Ishaan94 Group Title

what is exactly meant by order doesn't matter?

19. Ishaan94 Group Title

is 12 = 21 if order doesn't matter?

20. Zarkon Group Title

yes

21. Ishaan94 Group Title

how would you do it for 121212121 if order matters

22. Zarkon Group Title

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 Group Title

doesn't involve nPr or nCr?

24. Ishaan94 Group Title

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

25. Ishaan94 Group Title

I am bad at combinatorics :-/