Question

The number of $n$ digit numbers such that no two consecutive digits are same is

• A. $9!$
• B. $n^9$
• C. $9^n$
• D. $9n$

Answer 1

Answer: (C)

$9^n$

There are $\{0,1,2,.....10\},$ $10$ different digits of which $1^{st}$ place is filled in $9$ ways, $2^{nd}$ place in $9$ ways (since $0$ can be included and first digit is not repeated) and so on $n$ times.

Thus number of ways is $=9\times 9\times ............=9^n$