Each license plate in a certain state has six characters (with repeats allowed).Here are the possibilities for each character.Character PossibilitiesFirst The digits 1, 2, 3, or 4Second The 26 letters of the alphabetThird The 26 letters of the alphabetFourth The 10 digits 0 through 9Fifth The 10 digits 0 through 9Sixth The 10 digits 0 through 9How many license plates are possible in this state?
Question
Each license plate in a certain state has six characters (with repeats allowed).Here are the possibilities for each character.Character PossibilitiesFirst The digits 1, 2, 3, or 4Second The 26 letters of the alphabetThird The 26 letters of the alphabetFourth The 10 digits 0 through 9Fifth The 10 digits 0 through 9Sixth The 10 digits 0 through 9How many license plates are possible in this state?
Solution
To calculate the total number of possible license plates, we need to multiply the number of possibilities for each character together.
- For the first character, there are 4 possibilities (1, 2, 3, or 4).
- For the second character, there are 26 possibilities (the 26 letters of the alphabet).
- For the third character, there are also 26 possibilities (the 26 letters of the alphabet).
- For the fourth character, there are 10 possibilities (the digits 0 through 9).
- For the fifth character, there are also 10 possibilities (the digits 0 through 9).
- For the sixth character, there are also 10 possibilities (the digits 0 through 9).
So, the total number of possible license plates is 4 * 26 * 26 * 10 * 10 * 10 = 26,840,000.
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