How many codes consisting of a letter followed by 3 digits can be made if no digit can be used more than once?
26*10*9*8
This assumes the letter "O" is allowed. Often it is not, because of confusion with zero. IT also assumes case of the letters is indifferent. If case masters, then A and a will be different, so you double the number of codes available.
can you tell me how you got 9 and 8?
I get it 26 alphabets.
10 digits.
To find the number of codes consisting of a letter followed by 3 digits, where no digit can be used more than once, we need to consider the following:
1. Choose a letter: There are 26 letters in the English alphabet, so we have 26 choices for the letter.
2. Choose the first digit: There are 10 digits from 0 to 9. Since no digit can be used more than once, we have 10 choices for the first digit.
3. Choose the second digit: After choosing the first digit, there are only 9 digits left to choose from (excluding the digit already chosen). Therefore, we have 9 choices for the second digit.
4. Choose the third digit: After choosing the first and second digits, there are only 8 digits left to choose from. Hence, we have 8 choices for the third digit.
To find the total number of codes, we multiply the number of choices together:
Total number of codes = Number of letter choices × Number of choices for the first digit × Number of choices for the second digit × Number of choices for the third digit
Total number of codes = 26 × 10 × 9 × 8
Therefore, there are 26 × 10 × 9 × 8 = 18,720 different codes that can be made.
To find out how many codes consisting of a letter followed by 3 digits can be made, we need to consider two things: the number of letters and the number of digits.
1. Number of letters: There are 26 letters in the English alphabet.
2. Number of digits: Since no digit can be used more than once, we have to consider the counting principle of combinations. For the first digit, we have 10 options (0-9). For the second digit, once we have selected one digit, we can only choose from the remaining 9 digits. Similarly, for the third digit, since we have selected two digits, we can only choose from the remaining 8 digits.
To find the total number of codes, we multiply the number of options for each part. Therefore, the total number of codes can be calculated as follows:
26 (number of letters) * 10 (number of options for the first digit) * 9 (number of options for the second digit) * 8 (number of options for the third digit)
Multiplying these values gives us the final answer:
26 * 10 * 9 * 8 = 18,720
Therefore, there are 18,720 codes consisting of a letter followed by 3 digits if no digit can be used more than once.