License plates in the great state of Utah consist of 2 letters and 4 digits. Both digits and letters can repeat and the order in which the digits and letters matter. Thus, AA1111 and A1A111 are different plates. How many possible plates are there?Question options:non of the above36^626^2x10^4x1526x26x10x10x10x10

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) = 26Total number of digits (0,1,2..,9)= 10Total 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.