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∗3∗2∗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)…∗1 4!=4∗3∗2∗1 4!=24

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