# How many automobile license plates can be made if each plate contains two different letters followed by three different digits?

$\begin{array}{1 1}(A)\;468000\\(B)\;466000\\(C)\;467800\\(D)\;463000\end{array}$

Toolbox:
• $n!=n(n-1)(n-2)(n-3).......(3)(2)(1)$
No of letters =2
There are 26 letters so,with no repetition
$\Rightarrow$ There can be $26\times 25$
$\Rightarrow 650$
No of digits =3
There are 10 digits
Hence the no of digits with no repetitions
$\Rightarrow 10\times 9\times 8$
$\Rightarrow 720$
Total no of ways of making the plates =$720\times 650$
$\Rightarrow 468000$
Hence (A) is the correct answer.