Answer:
1,808,352,000 different license plates can be issued using this configuration
Step-by-step 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:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
Four letters
In the alphabet, there are 26 letters. In the place, there are 4. So permutations of 4 from a set of 26.
[tex]P_{(26,4)} = \frac{26!}{4!} = 358800[/tex]
Four digits
There are 10 digits. In the plate, there are four. So permutations of 4 from a set of 10
[tex]P_{(10,4)} = \frac{10!}{6!} = 5040[/tex]
Total
Multiplying these values
358800*5040 = 1,808,352,000
1,808,352,000 different license plates can be issued using this configuration
