how many three letter security codes can be made from 4 letters A,B,C,D without using a letter twice? For example, BAC and A,D,B are two such codes. Explain
To determine how many three-letter security codes can be made from the letters A, B, C, and D without repeating any letter, we can use the concept of permutations.
A permutation is an arrangement of objects in a specific order. In this case, we want to arrange three letters without repetition. The formula to calculate permutations without repetition is given by:
P(n, r) = n! / (n - r)!
Where P is the number of permutations, n is the total number of options available, and r is the number of items to choose. In this case, n is 4 (as we have four letters: A, B, C, and D), and r is 3 (as we need to choose three letters for the security code).
Now, let's plug these numbers into the formula:
P(4, 3) = 4! / (4 - 3)! = 4! / 1! = 4 * 3 * 2 * 1 / 1 = 24 / 1 = 24
Therefore, there are 24 different three-letter security codes that can be made using the letters A, B, C, and D without repeating any letter.