Question

what is the total number of different 10 letter arrangements that can be formed using the letters in the word suspicious?
75600
151200
302400
604800
3628800

Explanation:

Step1: Count total letters and duplicates

Word: SUSPICIOUS (10 letters). Duplicates: S(3), U(2); others unique.

Step2: Apply permutation formula

Formula: $\frac{n!}{n_1!n_2!...n_k!}$ where $n=10$, $n_1=3$ (S), $n_2=2$ (U).
Calculate: $\frac{10!}{3!2!} = \frac{3628800}{6×2} = 302400$

Answer:

302400