Final answer:
To determine the number of distinct 4-letter arrangements from the English alphabet, we use permutations, resulting in 358,800 possible combinations when no repetition of letters is allowed.
Step-by-step explanation:
The question relates to the number of possible 4-letter arrangements with distinct letters in the English language. To answer this, we rely on the concept of permutations since the order of the letters matters and repetition is not allowed. In mathematics, the number of permutations of 'n' distinct objects taken 'r' at a time is given by 'n! / (n-r)!' where '!' denotes factorial, which is the product of all positive integers less than or equal to the number.
For a 4-letter arrangement from the 26 letters of the English alphabet, we treat it as a permutation problem where 'n' is 26 (because there are 26 different letters) and 'r' is 4 (because we want to arrange 4 of them).
Using the permutation formula, we find the math to be '26! / (26 - 4)!' which simplifies to '26 * 25 * 24 * 23'. Therefore, there are 358,800 possible 4-letter arrangements with distinct letters in the English language.