How many different license plate number can be made using 2 letters followed by 4 digits selected from the digits 0-9
a) if letters and digits may be repeated?
b) if letters may be repeated, but digits may not be repeated?
c) if neither letters nor digits may re repeated?
it was suppose to say pre cal sorry
letters: usually do not use O.
Let N be number of letters, ten the number of numerals.
a) N*N*10^4
b) N*N*10!/(10-4)!
c) N!/(N-2)! * 10!/(10-4)!
a) If both letters and digits may be repeated, we can find the total number of possible combinations by multiplying the number of choices for each position.
For the first letter, we have 26 choices (since there are 26 letters in the English alphabet).
For the second letter, we also have 26 choices.
For each of the four digits, we have 10 choices (since there are 10 possible digits).
Therefore, the total number of possible license plate numbers is:
26 * 26 * 10 * 10 * 10 * 10 = 6,760,000
b) If letters may be repeated, but digits may not be repeated, we have 26 choices for the first letter, 26 choices for the second letter, 10 choices for the first digit, 9 choices for the second digit (since we can't repeat the first digit), 8 choices for the third digit, and 7 choices for the fourth digit.
Therefore, the total number of possible license plate numbers is:
26 * 26 * 10 * 9 * 8 * 7 = 1,757,760
c) If neither letters nor digits may be repeated, we have 26 choices for the first letter, 25 choices for the second letter (since we can't repeat the first letter), 10 choices for the first digit, 9 choices for the second digit, 8 choices for the third digit, and 7 choices for the fourth digit.
Therefore, the total number of possible license plate numbers is:
26 * 25 * 10 * 9 * 8 * 7 = 3,570,000
To find the number of different license plate numbers that can be made, we need to use counting principles such as permutations and combinations.
a) If letters and digits may be repeated, then we have 26 choices for each of the two letters (A-Z) and 10 choices for each of the four digits (0-9).
To find the total number of possibilities, we multiply the number of choices for each position:
Total possibilities = 26 * 26 * 10 * 10 * 10 * 10 = 6,760,000
So, there are 6,760,000 different license plate numbers that can be made when both letters and digits may be repeated.
b) If letters may be repeated, but digits may not be repeated, then we have 26 choices for each of the two letters (A-Z) and 10 choices for the first digit, 9 choices for the second digit, 8 choices for the third digit, and 7 choices for the fourth digit.
To find the total number of possibilities, we multiply the number of choices for each position:
Total possibilities = 26 * 26 * 10 * 9 * 8 * 7 = 3,326,400
So, there are 3,326,400 different license plate numbers that can be made when letters may be repeated, but digits may not be repeated.
c) If neither letters nor digits may be repeated, then we have 26 choices for the first letter, 25 choices for the second letter (since it can't be the same as the first one), 10 choices for the first digit, 9 choices for the second digit, 8 choices for the third digit, and 7 choices for the fourth digit.
To find the total number of possibilities, we multiply the number of choices for each position:
Total possibilities = 26 * 25 * 10 * 9 * 8 * 7 = 3,570,000
So, there are 3,570,000 different license plate numbers that can be made when neither letters nor digits may be repeated.