Final answer:
The total number of different arrangements of the three distinct fatty acids in a triglyceride molecule is 3, accounting for the symmetry of the molecule.
Step-by-step explanation:
A triglyceride molecule is composed of glycerol and three fatty acids. Given the three different fatty acids, labeled as (L), (O), and (P), they can be arranged in various ways due to the three available positions on the glycerol backbone. The positions on glycerol can be occupied by any one of the fatty acids, and since their arrangement matters, the situation calls for calculating permutations of these fatty acids.
To determine the total number of different arrangements (permutations) of the fatty acids in the triglyceride, each of the three positions on the glycerol backbone can be occupied by any one of the fatty acids. We use a simple permutation formula for arranging 'n' unique items into 'k' positions: P(n, k) = n! / (n-k)! For three unique fatty acids arranging into three positions, the formula would give us 3! / (3-3)! = 6 / 1 = 6 different arrangements. However, since the triglyceride molecule is symmetrical, arrangements that are mirror images of each other are indistinguishable in a linear molecule. Therefore, the number of distinguishable arrangements is half of the total permutations, leading to the answer of 6 / 2 = 3 different arrangements.
Therefore, the correct answer is option A (3).