Answer: The word "symbolism" contains 9 letters. To find the number of distinguishable ways to rearrange these letters, we can use the formula for the number of permutations of n objects, which is n! (n factorial).
However, in this case, there are repeated letters, specifically "s" and "m". To account for this, we need to divide the total number of permutations by the factorials of the number of times each repeated letter appears.
The letter "s" appears twice, so we divide by 2!. Similarly, the letter "m" also appears twice, so we divide by 2!.
Therefore, the number of distinguishable ways to rearrange the letters in the word "symbolism" is:
9! / (2! × 2!) = 362,880 / 4 = 90,720
So there are 90,720 distinguishable ways to rearrange the letters in the word "symbolism".