I am having problems with this problem.In the mythical kingdom of Permutatus, wizards have special 2-digit license plats, The first digit is greater than 6, and the second digit is odd. The two digits cannot be the same, How many different license plates are possible.

No. of digits > 6 : {7,8,9} i.e. 3 of them

odd digits: {1,3,5,7,9}, i.e. 5
Total = 3×5 = 15
However, subtract number of plates with identical digits. Figure out which plates there are and calculate the final numbers.

To determine the number of different license plates possible in the kingdom of Permutatus, we need to consider the restrictions given for the first and second digit of the license plate.

Step 1: Count the number of choices for the first digit
Since the first digit must be greater than 6, we have 9 options: 7, 8, or 9.

Step 2: Count the number of choices for the second digit
The second digit must be odd and different from the first digit. We have 5 options: 1, 3, 5, 7, or 9.

Step 3: Multiply the number of choices for each digit
To calculate the total number of possibilities, we multiply the number of choices for the first digit by the number of choices for the second digit.

9 options for the first digit × 5 options for the second digit = 45

Therefore, there are 45 different license plates possible in the mythical kingdom of Permutatus, considering the given restrictions.

To find the number of different license plates that are possible with the given conditions, we can break down the problem step by step:

Step 1: Determine the number of options for the first digit
The problem states that the first digit must be greater than 6. Since there are only 10 digits (0 to 9), the options for the first digit are 7, 8, and 9. Therefore, there are 3 possibilities for the first digit.

Step 2: Determine the number of options for the second digit
The problem states that the second digit must be odd. The odd digits between 0 and 9 are 1, 3, 5, 7, and 9. However, the problem also mentions that the two digits cannot be the same. So, when we choose the first digit, we have one less option for the second digit. For example, if the first digit is 7, we cannot choose 7 as the second digit. Therefore, there are only 4 options for the second digit.

Step 3: Determine the number of options for both digits
To find the total number of options for both digits, we multiply the number of options for the first digit by the number of options for the second digit. So, total options = 3 (options for the first digit) * 4 (options for the second digit) = 12.

Therefore, there are a total of 12 different license plates possible in the mythical kingdom of Permutatus with the given conditions.