Question

imagine a license plate created 3 uppercase letters followed by 3 digits(1-9) The license plate can repeat letters and numbers. How many unique license plates exist?

Answer 1

Hey dear here is the answer


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:
26×26=676

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

10×10×10=1000

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

26×26×10×10×10=676,000 possibilities.

Hope this helps.