Discrete Mathematics - Permutations/Combinations?

[aliaze1]

Homework Statement

A certain state issues a series of automobile license plates such that each license plate
must have 2 letters followed by three digits. An example license plate would be AD 025 .
If the letters and the digits cannot be repeated, how many different license plates can be
issued by the state?

(a) 468,000 (b) 486,720 (c) 46,800 (d) 1,300 (e) 67,600

Homework Equations

Rules of factorials?
(ex: 5! = 5*4*3*2*1)

The Attempt at a Solution

How would I go about this?

I was thinking (26*25) + (10*9*8), but that is not an available option

Thanks

 

[rock.freak667]

well think of it like this: If the first 2 must be letters...how many choices do you have to pick the first letter?26 right...and if you pick one letter out then you have 25 remaining..so from the 25 you can pick one for the 2nd letter. and then for the rest of numbers it should be picking 3 numbers from 10..where the order is important

 

[Integral]

Why did you choose to add the probabilities? Try multiplying.

 

[aliaze1]

Why did you choose to add the probabilities? Try multiplying.

I originally thought they were separate things...

Thanks!

 

[bondgirl007]

I got 468,000 by multiplying 26*25*10*9*8.

 

[aliaze1]

me2

I got 468,000 by multiplying 26*25*10*9*8.

thanks!