How many different 9 digit combination can be made using numbers one through nine?

Answer 1

This depends on whether the digits of the number can be repeated.... is 1123456 allowed, or do the digits all have to be different.

Another question is can there be a leading 0 (or string of 0s, if duplication is allowed)

So, working through the options, if no duplication is allowed, and the leading character cannot be 0,

then there are 9 choices when we pick the first digit, 9 when we pick the second, 8 when we pick the third, 7 for the 4th, 6 for the 5th, 5 for the 6th and 4 for the 7th.

9 x 9 x 8 x 7 x 6 x 5 x 4 = 544,320

If we can lead with a 0 then there are 10 ways to pick the first digit, then 9 for the second, and so on down to 4 for the 7th.

10 x 9 x 8 x 7 x 6 x 5 x 4 = 604,800

If the digits can be repeated, but we cannot start with leading 0s then there are 9 ways to pick the first, and then 10 for each of the other positions

9 x 10 x 10 x 10 x 10 x 10 x 10 = 9,000,000

If we can use a leading 0 then we can choose from 10 digits for all positions and that is

10 x 10 x 10 x 10 x 10 x 10 x 10 = 10,000,000

Answer 2

A total of 729 9^3 = 729 However, if order of the numbers is not a condition (e.g. 1,2,1 is considered same as 1,1,2): 9!/6! + 9!/7! + 9!/8! = 504 + 72 + 9 = 585

Answer 3

9^9 = 387420489 different digit combinations.

Answer 4

There are 3,628,800 different permutations that can be made when using the numbers 0 through 9, if each number is only used once in each combination.

Answer 5

9,999,999