SOLUTION: My computer password has a letter followed by 5 digits and then another letter. If there are no repeats, then how many possible such computer passwords are there?

Here is a sample computer password:

W83175D

Choose a letter to go where the W is any of 26 ways, then
Choose a digit to go where the 8 is any of 10 ways, then
Choose a digit to go where the 3 is any of the remaining 9 ways, then
Choose a digit to go where the 1 is any of the remaining 8 ways, then
Choose a digit to go where the 7 is any of the remaining 7 ways, then
Choose a digit to go where the 5 is any of the remaining 6 ways, then
Choose a letter to go where the D is any of the remaining 25 ways.

That's 26*10*9*8*7*6*25 = 19,656,000 possible computer passwords.

Edwin