Final answer:
There are 17 fundamental particles in the Standard Model of particle physics, including the Higgs boson but excluding the not yet observed graviton. Hence, neither Option a (12) nor Option b (15) is correct as provided in the question.
Step-by-step explanation:
The question you are asking relates to the Standard Model of particle physics, which is a theory that describes the fundamental particles and forces that govern them. When discussing how many first entry faculties or fundamental particles exist, it is important to note that the Standard Model currently includes 17 discovered particles. This count comprises six quarks, six leptons, four gauge bosons, and the Higgs boson. The graviton, which would be the particle that mediates the force of gravity, is theorized but has not yet been observed and is not included in the Standard Model.
Therefore, the answer to the question in your physics exam or assignment would be Option b, which is 17 fundamental particles, including the Higgs boson but excluding the graviton. Hence, neither of the provided options (a: 12 or b: 15) is correct if we include the Higgs boson.