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
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.