how many different license plates can be formed if each plate has 3 different digits followed by 3 different letters?*
There are a total of 10 digits (0-9) that can be used for the first three positions on the license plate.
Once a digit is used, it cannot be used again in the same plate.
There are a total of 26 letters (A-Z) that can be used for the last three positions on the license plate.
Similarly, once a letter is used, it cannot be used again in the same plate.
To calculate the total number of different license plates that can be formed, we can use the concept of permutations.
The number of ways to select and arrange 3 different digits from a set of 10 without repetition is given by:
10P3 = 10! / (10-3)! = 10! / 7! = 10 x 9 x 8 = 720
Similarly, the number of ways to select and arrange 3 different letters from a set of 26 without repetition is given by:
26P3 = 26! / (26-3)! = 26! / 23! = 26 x 25 x 24 = 15,600
To find the number of different license plates that can be formed, we will multiply these two values together:
720 x 15,600 = 11,232,000
Therefore, there are 11,232,000 different license plates that can be formed if each plate has 3 different digits followed by 3 different letters.
To find the number of different license plates that can be formed, we need to determine the number of choices for each digit and letter position and then multiply these choices together.
First, let's consider the number of choices for the first digit. Since we are looking for three different digits, there are 10 possible choices for the first digit (0-9).
For the second digit, there are 9 remaining choices since we cannot repeat the digit chosen for the first position.
Similarly, for the third digit, there are 8 remaining choices.
For the first letter position, we have 26 choices since there are 26 letters in the English alphabet.
For the second letter position, there are 25 remaining choices since we can't repeat the letter chosen for the first position.
Similarly, for the third letter position, there are 24 remaining choices.
To find the total number of license plates that can be formed, we multiply the number of choices for each position together:
10 choices for the first digit x 9 choices for the second digit x 8 choices for the third digit x 26 choices for the first letter x 25 choices for the second letter x 24 choices for the third letter.
So, the number of different license plates that can be formed with three different digits followed by three different letters is:
10 x 9 x 8 x 26 x 25 x 24 = 6,595,200.