How many different license plates begin with two digits followed by two letters

A witness to a hit-and-run accident tells the police that the license plate of the car in the accident, which contains three letters followed by three digits, starts with the letter A and contains both the digits 1 and 2. How many different license plates can fit this description?

There is nothing stating that the letters and numbers can't be repeated, so all#26#letters of the alphabet and all#10#digits can be used again.

If the first is A, we have#26#possibilities:
AA, AB, AC,AD,AE ...................................... AW, AX, AY, AZ.

If the first is B, we have#26#possibilities:
BA, BB, BC, BD, BE .........................................BW, BX,BY,BZ

And so on for every letter of the alphabet.

There are#26#choices for the first letter and#26#choices for the second letter. The number of different combinations of#2#letters is:
#26 xx 26 = 676#

The same applies for the three digits.
There are#10#choices for the first,#10#for the second and#10#for the third:

#10xx10xx10 =1000#

So for a license plate which has#2#letters and#3#digits, there are:

#26xx26xx10xx10xx10= 676,000#possibilities.

Hope this helps.

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  How many license plates can be made with 2 letters and 2 digits?

  2 Answers By Expert Tutors since repetition is allowed the number of licence plates you could make is 4.

  How many license plates can be made so that it begins with two letters and ends with five digits repetitions are allowed?

  The alphabet contains 26 letters, so a two digit combination gives you 26 by 26 = 676 choices. A five digit number gives you 100,000 different variants, given the rule that shorter than five digit numbers are either allowed or filled up with zeros, so you take 001234 instead of 1234.

  How many automobile license plates can be made involving 2 letters followed by 3 digits?

  So, we can calculate total number license plates that can be made with 2 letters and then 3 digits using fundamental counting principle. Total number of license plates that can be formed is 676000.