How many different structures (including stereoisomers) are possible for a triglyceride that contains one palmitic acid residue, one arachidic acid residue and one stearic acid residue?

Question

Quizplus · Accepted Answer

There are 3 different fatty acids involved in the triglyceride: palmitic acid (16 carbon chain), arachidic acid (20 carbon chain), and stearic acid (18 carbon chain). 
For each fatty acid, there are 2 possible stereoisomers (cis and trans) for the unsaturated bonds.
Thus, the total number of possible structures (including stereoisomers) is:
2 (stereoisomers of palmitic acid) x 2 (stereoisomers of arachidic acid) x 2 (stereoisomers of stearic acid) = 8
However, since the triglyceride only contains one of each fatty acid, we must divide by 3! (the number of permutations of the fatty acids) to avoid overcounting:
8 / 3! = 8 / 6 = 1.33, which rounds up to 2. 
Therefore, there are a total of 2 possible structures for the triglyceride.

How Many Different Structures (Including Stereoisomers) Are Possible for a Triglyceride