Final answer:
The total number of different 10-letter arrangements that can be formed from the word SUSPICIOUS is 151200. This is calculated using the permutations formula for a multiset, considering the repeated letters in the word.
Step-by-step explanation:
The student is asking about the number of different 10-letter arrangements that can be formed from the word SUSPICIOUS. To solve this, we must use permutations accounting for repeated letters. The word SUSPICIOUS consists of 10 letters, with 'S' repeating 3 times, 'U' repeating 2 times, and 'I' repeating 2 times.
Using the formula for permutations of a multiset, the total number of unique arrangements is:
Total arrangements = 10! / (3! × 2! × 2!)
Where 10! (ten-factorial) is the number of ways to arrange 10 letters, and 3!, 2!, and 2! are the factorial counts of the repeated letters 'S', 'U', and 'I', respectively.
Calculating this gives:
10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
3! = 3 × 2 × 1
2! = 2 × 1
Thus, the total number of arrangements = 3628800 / (6 × 2 × 2) = 151200. Hence, there are 151200 different 10-letter arrangements that can be formed using the letters in the word SUSPICIOUS.