Answer:
The correct option is 3.
Step-by-step explanation:
It is given that License plates in the great state of Utah consist of 2 letters and 4 digits.
Total number of letters (A,B,...,Z) = 26
Total number of digits (0,1,2..,9)= 10
Total ways to select a letter is 26 and total ways to select a digit is 10. So, total number of ways to select 2 letter and 4 digits is
[tex]26\times 26\times 10\times 10\times 10\times 10=26^2\times 10^4[/tex]
Total ways to arrange these two 2 letter and 4 digits are
[tex]\frac{6!}{4!2!}=15[/tex]
Because total number of places are 6. In which letter can be repeated 2 times and digit can be repeated 4 times.
Total possible plates are
[tex]26^2\times 10^4\times 15[/tex]
Therefore the correct option is 3.
