How Many Possible Passwords Can Be Created with 5 Unique Letters?

When creating a computer password with 5 letters where no letter can be repeated, the key factor to consider is the concept of permutations. In mathematics, a permutation is an arrangement of objects in a specific order. In this case, the objects are the letters that can be used for the password.

To calculate the number of possible passwords, we can use the formula for permutations of n objects taken r at a time, which is denoted as P(n, r) = n! / (n - r)!. In our scenario, n represents the total number of unique letters available and r is the number of letters to be used in the password.

With 26 letters in the English alphabet, if we choose 5 unique letters for the password, the calculation would be as follows:

P(26, 5) = 26! / (26 - 5)! = 26! / 21!

Solving the above equation gives us a total of 65,780 possible unique passwords that can be created using 5 letters without repetition.