Question

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...

Answer 1

`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.