How many different license plates are possible If each contains 2 lotters (out of the alphabet's 26 letters) followed by 4 digits (from 0 to 9 )? How many of these license plates contain no repeated letters and no repeated digits? There are $\square$ diflerent possible license plates. (Simplify your answer) There are $\square$ different possiblo license plates if no letters or numbers are repoated. (Simplify your answer.)

Step 1 ：The first part of the question is asking for the total number of possible license plates, given that each plate contains 2 letters (from a pool of 26) followed by 4 digits (from 0 to 9). This is a permutation problem, as the order of the letters and numbers matters. The formula for permutations is nPr = n! / (n-r)!, where n is the total number of options, r is the number of options chosen, and ! denotes factorial. However, since we are choosing all available options (i.e., we are not choosing a subset), the formula simplifies to n!, or the product of all positive integers up to n.

Step 2 ：The second part of the question is asking for the number of possible license plates if no letters or numbers are repeated. This is also a permutation problem, but now we are choosing a subset of the available options. We can use the nPr formula for this part of the question.

Step 3 ：Let's calculate these two values. The total number of possible license plates is \(26^2 * 10^4 = 6760000\), and the number of possible license plates with no repeated letters or numbers is \(26P2 * 10P4 = 3276000\).

Step 4 ：Final Answer: There are \(\boxed{6760000}\) different possible license plates. There are \(\boxed{3276000}\) different possible license plates if no letters or numbers are repeated.