How many license plates can be made consisting of 2 letters followed by 3 digits (using the fundamental counting principle to solve)?

What I know:

  • 26 letters in alphabet, so that means 2xx26
  • 10 digits possible (0-9), so that means 3xx10
  • FC principle says given m and n options gets you mxxn varieties...
    ... However, the answer key says "676,000" when I got 1560...

1 Answer
EZ as pi
Jul 11, 2017

26xx26xx10xx10xx10= 676,000 possibilities

Explanation:

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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