Answer:
3,276,000 possible license plates for this state
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]
Letters
There are 26 letters in the alphabet. In the plate, there are two letters. So permutations of two from a set of 26.
[tex]P_{(26,2)} = \frac{26!}{24!} = 650[/tex]
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
650*5040 = 3,276,000
3,276,000 possible license plates for this state
