Final answer:
The number of 5-letter words formed with at least one repeated letter from ten different letters is 30240. This is found by subtracting the number of permutations of 10 letters taken 5 at a time from the total number of possible words without any restrictions. The correct answer is B.
Step-by-step explanation:
The question concerns the number of 5-letter words that can be formed with at least one repeated letter from a set of ten different letters. To solve this, we use the principle of counting. First, we calculate the total number of 5-letter words that can be formed with ten different letters without any restriction, which is the permutation of 10 letters taken 5 at a time (10P5). Then, we calculate the number of 5-letter words with all unique letters, which is the permutation of 10 letters taken 5 at a time without repetition (10P5 = 10!/(10-5)!).
Then, we subtract the number of 'all-unique-letter' words from the total number of possible words to get the number of words with at least one repeated letter. Using the formula for permutation, 10P5 = 10 × 9 × 8 × 7 × 6.
Hence, the total number of possible words without restriction is 10^5. After performing the calculation, we find that the number of words with at least one repeated letter is 30240, which corresponds to answer choice B.