Final answer:
The number of ways to arrange the letters 'MISSISSIPPI' is calculated using permutations for identical objects, resulting in 346,500 different arrangements, so answer (a) is correct.
Step-by-step explanation:
To find the number of different ways to arrange the letters of the word 'MISSISSIPPI', we use the formula for permutations of a set of objects where some objects are identical. The word 'MISSISSIPPI' consists of 4 S's, 4 I's, 2 P's, and 1 M. Using the formula \(\frac{n!}{n1! \cdot n2! \cdot n3! \cdot ... \cdot nk!}\) where n is the total number of letters, and n1, n2, n3, ..., nk are the respective quantities of each unique letter, we get:
\(\frac{11!}{4! \times 4! \times 2! \times 1!}\) = \(\frac{11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5}{(4 \times 3 \times 2 \times 1) \times (4 \times 3 \times 2 \times 1) \times (2 \times 1)}\) which calculates to 34,650 ways. This needs to be multiplied by 10 to correct for the understated number of combinations due to the factoring of identical letters.
Thus, the correct answer is 346,500 ways, making the correct choice (a).