Question

The state of Georgia ran out of unique license plates in 2010. Prior to 2010, the license plates were formulated using the style LLLDDD, where L is any letter of the alphabet excluding vowels and Q, and D is a digit between 0 and 9. The new style introduced is in the form LLDDLL. How many more possible number plates are there using the new style when compared to the old style?

Answer 1

To determine the difference in the number of possible number plates using the new style compared to the old style, we need to find the number of possible plates for each style and subtract them. The old style allows for 9,261,000 possible plates, while the new style allows for 960,400 possible plates. Therefore, there are 8,300,600 more possible number plates using the new style compared to the old style.

Step-by-step explanation:

To determine how many more possible number plates there are using the new style compared to the old style, we need to find the number of possible plates for each style and compare them.

For the old style, there are 21 choices for each letter (since vowels and Q are excluded) and 10 choices for each digit. So, there are a total of 21*21*21*10*10*10 = 9,261,000 possible plates.

For the new style, there are 21 choices for each letter and 10 choices for each digit, making a total of 21*21*10*10*21*21 = 960,400 possible plates.

Therefore, there are 9,261,000 - 960,400 = 8,300,600 more possible number plates using the new style compared to the old style.