Question

Suppose in a state, license plates have two letters followed by four numbers, in a way that no letter or number is repeated in a single plate. Determine the number of possible license plates for this state

Answer 1

3,276,000 possible license plates for this state

Explanation:

The order is important. For example, if the letters are EM, it is already a different plate than if the letters were ME. So we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

`P_((n,x)) = (n!)/((n-x)!)`

Letters

There are 26 letters in the alphabet. In the plate, there are two letters. So permutations of two from a set of 26.

`P_((26,2)) = (26!)/(24!) = 650`

Digits

There are 10 digits. In the plate, there are four. So permutations of 4 from a set of 10

`P_((10,4)) = (10!)/(6!) = 5040`

Total

Multiplying these values

650*5040 = 3,276,000

3,276,000 possible license plates for this state