Final answer:
To find the number of license plates in different scenarios, consider the choices for each position in the format. If repetition is allowed, multiply the number of choices. If repetition is not allowed, reduce the choices with each position.
Step-by-step explanation:
To find the number of license plates that can be created using the D..DL.. L-format, we need to consider the different possibilities for each position in the format.
i. If repetition of digits and letters is allowed: There are 5 odd digits and 5 capital vowel letters. So, for each position, there are 5 choices. Therefore, the total number of license plates that can be created is 5*5*5 = 125.
ii. If repetition of digits is allowed but repetition of letters is not allowed: In this case, there are still 5 choices for each position for the odd digits, but only 4 choices for the capital vowel letters. Therefore, the total number of license plates that can be created is 5*5*4 = 100.
iii. If repetition of digits is not allowed but repetition of letters is allowed: In this case, there are 5 choices for the first odd digit, 4 choices for the second odd digit (as repetition is not allowed), and 5 choices for each capital vowel letter. Therefore, the total number of license plates that can be created is 5*4*5*5 = 500.
iv. If repetition of digits and letters is not allowed: In this case, there are 5 choices for the first odd digit, 4 choices for the second odd digit, 5 choices for the first capital vowel letter, and 4 choices for the second capital vowel letter. Therefore, the total number of license plates that can be created is 5*4*5*4 = 400.