How many different passcodes can be formed from the letters {A, B, C, D} if each letter can only be used once?

Explanation

Given that each letter can only be used once, and there are a total of 4 letters, the first character of the passcode can only be occupied by 4 different letters. After using the first letter, there are 3 letters remaining that can occupy the second spot; then 2 letters for the third spot, and only 1 letter for the last spot. The product of these values yields the total number of possibilities:

\(4 \times 3 \times 2 \times 1=24\)

The solution can also be found using the formula for the total number of different arrangements of n distinct elements:

\(n !=n(n-1)(n-2) \ldots \times1\)

\(4 !=4 \times 3 \times 2 \times 1\)

4!=24

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