A password consists of three digits, 0 through 9, followed by three letters from an alphabet having 26 letters.

If repetition is allowed but repitition of letter is not allowed, determine the # of different passwords that can be made.

I have....
10*10*10*26*25*24=15600000...........is that right???

correct.

To determine the number of different passwords that can be made, we need to calculate the product of the number of possibilities for each position in the password.

Assuming repetition is allowed for digits but not for letters:

For the first digit, there are 10 possibilities (0 through 9).
For the second digit, there are also 10 possibilities.
For the third digit, there are again 10 possibilities.

For the first letter, there are 26 possibilities (all the letters of the alphabet).
For the second letter, since repetition is not allowed, there are 25 possibilities remaining after choosing the first letter.
For the third letter, there are 24 possibilities remaining after choosing the first two letters.

So the total number of different passwords that can be made is:

10 * 10 * 10 * 26 * 25 * 24 = 15,600,000

Therefore, your calculation is correct. The number of different passwords that can be made is indeed 15,600,000.

To determine the number of different passwords that can be made, we need to consider each part separately.

1. For the first three digits, we have 10 choices for each digit (0 through 9). Since repetition is allowed, we multiply the choices together: 10 * 10 * 10 = 1000.
2. For the next three letters, we have 26 choices for the first letter of the alphabet and 25 choices for the second letter (since repetition of letters is not allowed). For the third letter, we have 24 choices (as repetition is not allowed). So, we multiply these choices together: 26 * 25 * 24 = 15,600.

To obtain the total number of different passwords, we multiply the number of choices for each part together: 1000 * 15,600 = 15,600,000.

Therefore, the correct answer is 15,600,000, which is the number of different passwords that can be made. Your calculation of 15,600,000 is correct.