What are the possible combinations of multiple bonds and rings if a compound's index of hydrogen deficiency equals 3?

Question

Quizplus · Accepted Answer

If a compound's index of hydrogen deficiency equals 3, then there are three fewer H atoms than in the corresponding saturated hydrocarbon with the same number of C atoms. The index of hydrogen deficiency equation is:
Index of Hydrogen Deficiency = [2n + 2 - (2a + b)]/2
where n is the number of carbons, a is the number of hydrogens, and b is the number of heteroatoms (including nitrogen and halogens).
So, for a compound with an index of hydrogen deficiency equal to 3 and no heteroatoms, we have:
2n + 2 - 2a = 6
n - a = 2
This means that there are two sites of unsaturation in the molecule, which could be two double bonds or one ring and a double bond or two rings. The only answer choice that includes all three possible combinations is C: three rings; two rings and a double bond; one ring and two double bonds; one ring and one triple bond.

What Are the Possible Combinations of Multiple Bonds and Rings