In a certain state, each automobile license plate number consists of two letters followed by a four-digit number. To avoid confusion between "O" and zero and between "I" and one, the letters "O" and "I" are not used. How many distinct license plates can be formed in this state?
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To determine the number of distinct license plates that can be formed in this state, we need to consider the possible combinations of letters and digits.
Since there are 24 letters available (excluding "O" and "I"), and each license plate consists of two letters followed by four digits, we can calculate as follows:
Number of distinct license plates = Possible letter combinations * Possible digit combinations
Possible letter combinations = 24 * 24 (since there are 24 options for each of the two letter slots)
Possible digit combinations = 10 * 10 * 10 * 10 (since each digit can be any number from 0 to 9)
Therefore, the number of distinct license plates that can be formed in this state is:
Number of distinct license plates = 24 * 24 * 10 * 10 * 10 * 10
= 576,000
So, there can be a total of 576,000 distinct license plates formed in this state.
To find the number of distinct license plates that can be formed in this state, we need to consider the number of choices for each position on the plate.
For the first two letters, there are 24 choices since two letters ("O" and "I") are not used.
For the four-digit number, each digit has 10 choices (0-9).
Therefore, the total number of distinct license plates that can be formed is:
24 choices for the first letter x 24 choices for the second letter x 10 choices for each digit in the four-digit number.
So, the answer is:
24 x 24 x 10 x 10 x 10 x 10 = 5,760,000 distinct license plates.
26 letters - 2 = 24 letters
choice of 24 letters for first letter
since letters can be repeated we have 24*24 = 576 letter combinations
now we have ten numbers, 0 through 9
again they can be repeated
(AA0000 is allowed)
10^4 = 10,000
so
576 * 10,000 = 5.76 * 1,000,000
= 5,760,000
Well, let's break it down. Since there are 26 letters in the alphabet, and we're excluding "O" and "I," we have 24 letters to choose from for the first two positions. That gives us 24 * 24 = 576 possible combinations for the letters.
As for the last four positions, we have ten digits to choose from (0-9). So there are 10 * 10 * 10 * 10 = 10,000 possible combinations for the digits.
To get the total number of distinct license plates, we multiply the number of combinations for the letters by the number of combinations for the digits: 576 * 10,000 = 5,760,000.
So, in this state, there are 5,760,000 distinct license plates that can be formed. That's a lot of cars to keep track of!