In Utah, a license plate consists of 3 digits followed by 3 letters. The letters I, O, and Q are not used, and each digit or letter may be used more than once. How many different license plates are possible?
I am assuming that the zero can be used in any of the 3 opening places.
e.g. 000ABC should be ok and we can only use 23 of the 26 letters.
so 10x10x10x23x23x23 = 12167000
To find the number of different license plates possible in Utah, we need to consider the number of choices for each digit and each letter in the license plate.
First, let's calculate the number of choices for the digits. Since each digit may be used more than once, we have 10 choices for each digit (0-9). Therefore, there are 10 choices for each of the 3 digits.
Next, let's calculate the number of choices for the letters. Since we cannot use the letters "I", "O", or "Q", we have 23 choices for each letter (26 letters - 3 prohibited letters). Therefore, there are 23 choices for each of the 3 letters.
To find the total number of combinations, we multiply the number of choices for each digit and each letter together:
Total number of combinations = Number of choices for digits × Number of choices for letters
= 10 × 10 × 10 × 23 × 23 × 23
= 1,871,000
Therefore, there are 1,871,000 different license plates possible in Utah.
To find the number of different license plates possible in Utah, we need to determine the number of options for each position.
There are 3 positions for digits and 3 positions for letters.
For the digit positions, we can use any of the 10 digits (0-9). Since a digit can be used more than once, there are 10 options for each digit position.
For the letter positions, we have 23 letters to choose from (26 letters - 3 prohibited letters I, O, Q). Again, since a letter can be used more than once, there are 23 options for each letter position.
Therefore, the total number of different license plates possible is calculated by multiplying the options for each position together:
10 (options for the first digit) * 10 (options for the second digit) * 10 (options for the third digit) * 23 (options for the first letter) * 23 (options for the second letter) * 23 (options for the third letter)
So, the number of different license plates possible in Utah is:
10 * 10 * 10 * 23 * 23 * 23 = 1,113,900