Question

Discrete math (please have legible handwriting).

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

Answer 1

Solution:

The first letter can be chosen in 26 ways

For Given that the second letter can be chosen in 25 ways

Since repetition is not allowed, the first letter chosen cannot be re-selected.

If three digits selected

the third digit can be chosen in 10 ways 0 to 9

the fourth digit can be chosen in 9 ways, Since repetition is not allowed, the 3rd digit chosen can't be re-selected.

the fifth digit can be chosen in 8 ways, Since repetition is not allowed, the 3rd and 4th digits chosen can't be re-selected.

So the total number of cases is = 26*25*10*9*8 = 468000

If 4 digits selected

the total number of cases is =26*25 * 10 * 9 * 8 * 7 =3276000