Question

In a certain state, license plates each consist of 2 letters followed by either 3 or 4 digits. How many differen license plates are there that have no repeated letters or digits?

Answer 1

26 × 26 × 10 × 10 × 10 = 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 × 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.