A bicycle lock has three rings with a letter A through K on each ring. To unlock, a letter must be selected on each ring. Duplicate numbers are not allowed, and the order in which the letters are selected does not matter. In how many ways can this bicycle lock be set

1 answer

Since duplicate letters are not allowed and the order doesn't matter, we simply need to count the number of ways to select three distinct letters from the letters A through K.

There are 11 options for the first letter, 10 options for the second letter (since one has already been chosen), and 9 options for the third letter (since two have already been chosen).

Therefore, there are 11 * 10 * 9 = <<11*10*9=990>>990 ways to set the bicycle lock.