To determine the number of different arrangements of 5 letters from the 26 letters of the alphabet, we can use the concept of permutations. Since the order of the letters matters (for example, ‘ABCDE’ is different from ‘EDCBA’), we will calculate permutations.
The number of ways to arrange ‘n’ items taken ‘r’ at a time (where order matters) is given by the formula:
P(n, r) = n! / (n – r)!
In our case, ‘n’ is 26 (the total number of letters in the alphabet) and ‘r’ is 5 (the number of letters we want to arrange).
Plugging in the values, we get:
P(26, 5) = 26! / (26 – 5)! = 26! / 21!
Now, we simplify that:
P(26, 5) = 26 × 25 × 24 × 23 × 22
This calculation yields:
P(26, 5) = 7893600
Thus, there are 7,893,600 different arrangements of 5 letters that can be made from the 26 letters of the alphabet.