Question

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

Answer 1

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

Answer 2

Too many to count would be my best guess.

Answer 3

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

Answer 4

Order doesn't matter and there's repetition

Answer 5

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

Answer 6

grrr

Answer 7

That doesn't really help

Answer 8

9! so it would be 9x8x7x6x5x4x3x2x1=362880

Answer 9

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

Answer 10

no it shouldnt

Answer 11

Zarkon...any input at all??

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

if you wanted to arrange 112223333

\[\frac{9!}{2!3!4!}\]

Answer 17

multinomial coefficients

Answer 18

what is exactly meant by order doesn't matter?

Answer 19

is 12 = 21 if order doesn't matter?

Answer 20

yes

Answer 21

how would you do it for 121212121 if order matters

Answer 22

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.

Answer 23

doesn't involve nPr or nCr?

Answer 24

hmm 5 1s and 4 2s total 9 position

is it \[\frac{9!}{4!} + \frac{9!}{5!}\]? (order matters)

Answer 25

I am bad at combinatorics :-/