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Find the total number of n -digit number...

Find the total number of `n` -digit number `(n >1)` having property that no two consecutive digits are same.

Text Solution

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Place `x_(1)` can be filled in 9 ways as digit '0' cannot be used.
Place `x_(2)` can be filled in 9 ways as '0' can be used but digit of place `x_(1)` cannot be used.
Similarly, each of the remaining places can be filled in 9 ways.
Thus, total number of such numbers `= 9xx9xx9`.. n times `=9^(n)`.
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