# Easy Permutation-Combination Solved QuestionAptitude Discussion

 Q. Find  the  total  number  of  distinct  vehicle  numbers  that  can  be  formed  using  two letters followed by two numbers. Letters need to be distinct.
 ✖ A. $60,000$ ✔ B. $65,000$ ✖ C. $70,000$ ✖ D. $75,000$

Solution:
Option(B) is correct

Out of $26$ alphabets two distinct letters can be chosen in ${^{26}P_2}$ ways.

Coming to numbers part, there are $10$ ways (any number from $0$ to $9$ can be chosen) to choose the first digit and similarly another $10$ ways to choose the second digit.

Hence, there are totally $10×10 = 100$ ways.

Combined with letters there are ${^{26}P_2}× 100 = \textbf{65000}$ ways to choose vehicle numbers.

## (1) Comment(s)

Swetha
()

Why can't the alphabets be same. Why should be they distinct.

(eg. AA00)

26 X 26 X 10 X 10 = 67600