We can choose the first digit in any of 9 ways, 1,2,3,4,5,6,7,9 or 9 .
We can then choose the second digit in any of the 9 ways, 0 or any of 8 ways not chosen for the first digit.
We can then choose the third digit in any of the 9 ways, other than the second digit.
We can choose the fourth digit in any of the 9 ways, other than the third digit.
And we can choose the fifth digit in any of the 9 ways, other than fourth digit.
Hence number of ways = 9*9*9*9*9 = [tex]9^{5} = 59049[/tex]
So, total number of five digit numbers which don't have consecutive digits same is 59049.
