How many license plates...

Question

How many license plates can be produced using five symbols on each plate where the two first symbols are letters of the alphabet and the following three symbols are numbers selected from the set {0,1,2,3,4,5,6,7,8,9}? No number or letter can be repeated on the same license plate.

Answer 1

Hi Shelby

 

You solve this by asking yourself the question how many choices do I have for the next symbol or letter and then multiplying all choices together.

 

So for the first symbol you can choose from the letters of the alphabet

 

Therefore 26 choices

 

Now since you have used one letter you will only have 25choices for the second symbol

 

For the numbers you only have 10 choices for the first pick

 

9 for the second

 

8 for the third

 

Then you multiply all the numbers 

 

26 * 25 * 10 * 9 * 8.  

 

 

You can do the multiplication but hopefully you understand the process

 

Hope this helps

 

Tom