Final answer:
Idiopathic thrombocytopenic purpura (ITP) is characterized by a low platelet count, leading to symptoms like petechiae, easy bruising, and bleeding gums due to thrombocytopenia. Therefore, the correct option is c.
Step-by-step explanation:
The condition that would have the following clinical manifestations: petechiae, easy bruising, bleeding gums, and a platelet count of 75,000/μl is Idiopathic thrombocytopenic purpura (ITP). This is a disorder characterized by a low platelet count, known as thrombocytopenia, which results in the inability of blood to form clots properly, leading to excessive bleeding. ITP is considered an autoimmune disease where the body's immune system mistakenly attacks and destroys its own platelets. In contrast, conditions such as thrombocytosis involve an excessive number of platelets, increasing the risk for clot formation, or thrombosis, rather than bleeding.