How many different license plates are possible if each contains letters out of the alphabet 26 letters followed by digits from 0 to 9 )?

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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  if you assume small letters and big letters can be used, then the number of possible license places will be 52^4 * 10^2 = 731,161,600.

  nomall, only capital letters are used, so your answer should be 45,697,600 license plates can be issued.

  

  Arthur D. answered • 03/12/15

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  if the characters can be repeated...

  26*26*26*10*10*10=17,576,000

  if the characters cannot be repeated...

  26*25*24*10*9*8=11,232,000

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  How many license plates can be made consisting of 3 letters 26 letters in the alphabet followed by 2 digits 0 9 )?

  Summary: 1757600 license plates can be made consisting of 3 letters followed by 2 digits.

  How many different license plates are available if each plate contains a sequence of 4 letters followed by 2 digits?

  So the answer is computed as: 26x26x26x26x10x10. Therefore, there are 45,697,600 possible license plates given the constraints in the question.

  How many license plates in a format of 3 letters and 4 digits are possible?

  Hence the number of possible plates is ${{26}^{3}}\times {{10}^{4}}=17,57,60,000$. Note: Generally, we can see that the letters and digits in the number plates are repeated, so we have not considered the reputation.

  How many license plates are possible if each plate contains a sequence of three letters starting with d followed by four digit non zero number?

  So, the correct answer is “468000”.