SOLUTION: how many five-digit numbers have no two consecutive digits equal. please answer and provide how you got it.

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Question 584947: how many five-digit numbers have no two consecutive digits equal.
please answer and provide how you got it.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
We can choose the first digit any of 9 ways, 1,2,3,4,5,6,7,8 or 9

We can then choose the 2nd digit any of 9 ways, 0 or any of 8 ways not chosen for the 1st digit

We can then choose the 3rd digit any of the 9 ways we didn't choose for 2nd digit.

We can then choose the 4th digit any of the 9 ways we didn't choose for the 3rd digit.

We can then choose the 5th digit any of the 9 ways we didn't choose for the 4th digit.

That's 9򊷹򊷹 = 95 = 59049

Edwin