How many different four-letter permutations can be formed using four letters out of the first twelve in the alphabet?

To find the number of different four-letter permutations that can be formed using four letters from the first twelve letters of the alphabet (A-L), you would use the permutation formula \( P(n, r) = \frac{n!}{(n - r)!} \), where \( n \) is the total number of items to choose from and \( r \) is the number of items to choose. In this case, \( n = 12 \) and \( r = 4 \). So, the calculation is \( P(12, 4) = \frac{12!}{(12 - 4)!} = \frac{12!}{8!} = 12 \times 11 \times 10 \times 9 = 11,880 \). Therefore, there are 11,880 different four-letter permutations possible. If you want to explore this concept further, try figuring out how many combinations you can make instead of permutations. Combinations don't care about the order of the letters, which can lead to a fascinating comparison of how many different ways you can arrange the same sets of letters. Often, people confuse combinations with permutations and mistakenly think they’re the same. Remember, permutations are all about the order (like arranging a race), while combinations are about the selection (like choosing your team). Keep that in mind to avoid mixing them up next time you’re in a tough spot!