A certain state makes license plates with any three digits followed by any three letters. How many different license plates can be made?
17)
______
A)
17,576,000
B)
9
C)
11,232,000
D)
12,812,904
There are 26 choices in each letter, and 10 choices in each digit.
By the multiplication principle, the total number of choices for a 3-letter followed by 3-digits is therefore 26*26*26*10*10*10
=26³*10³
17,576,000 : repeating
11,232,000 : not repeating
To find the number of different license plates that can be made, we need to calculate the number of possible combinations for both the digits and the letters.
For the digits, we have any three digits from 0 to 9. Since repetition is allowed, we have 10 options for each digit, giving us a total of 10 * 10 * 10 = 1,000 possible combinations.
For the letters, we have any three letters of the alphabet. There are 26 letters in the English alphabet, and repetition is allowed, so we have 26 options for each letter, giving us a total of 26 * 26 * 26 = 17,576 possible combinations.
To find the total number of license plates, we multiply the number of digit combinations (1,000) by the number of letter combinations (17,576):
1,000 * 17,576 = 17,576,000
Therefore, the correct answer is A) 17,576,000.