Combinatorics and Permutations

Question

If a license plate has three letters followed by two numbers and ending with either a P or a D, how many plates can be made that are all different.
Do not use any commas in your answer.
(An example would be a plate with the following letters and numbers: ERM 23 P)

Answer 1

The first three positions can each be any letter so there are 26 choices for each of these positions.

 

The next two can each have any digit, so there are 10 choices for each of these positions.

 

The last position can be a P or D so there are 2 choices for it.

 

The choices for all positions are independent, so use the multiplication rule.

 

Number of Plates possible: N = 26³10²2 = 3515200.

Answer 2

Alison,

 

Each license place has the form ABC##P or ABC##D, where A, B, and C can be ANY of the 26 letters in the English alphabet and # can be any of the 10 digits 0 through 9.

 

Since there are 26 letters and 10 digits and two possible last letters, there are a total of

 

26³ · 10² · 2 = 3,515,200 possible license plates.

 

Let me know if you have any questions.