Permutation-Combination
Aptitude

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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.

$75,000$

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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.


(2) Comment(s)


Shaan
 ()

Having the same doubt. I guess the answer given in incorrect.

It should have been 26*26*10*10=67600



Swetha
 ()

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

(eg. AA00)

26 X 26 X 10 X 10 = 67600