Study of Efficacy and Safety of Grazoprevir (MK-5172) + Elbasvir (MK-8742) With or Without Ribavirin for Participants With Hepatitis C Genotype 1, 4, or 6 Infections Who Have Failed Prior Treatment With Pegylated Interferon + Ribavirin (MK-5172-068)

Inclusion Criteria: * Documented chronic HCV GT1, GT4, or GT6 with no evidence of non-typable or mixed genotype infection (positive for anti-HCV antibody, HCV ribonucleic acid \[RNA\], or any of the listed GTs at least 6 months prior to screening must be confirmed by screening lab results) * Cirrhosis defined as liver biopsy showing METAVIR F4; or Fibroscan showing result \>12.5 kilopascals (kPa); or FibroSure® (Fibrotest®) score of \>0.75 and an aspartate aminotransferase (AST):platelet ratio index (APRI) of \>2 * Absence of cirrhosis defined as liver biopsy showing absence of cirrhosis; or Fibroscan result of ≤ 12.5 kPa; or Fibrosure® (Fibrotest®) score of ≤ 0.48 and APRI ≤ 1 * Previous HCV treatment status of peginterferon/RBV Null responder; or peginterferon/RBV Partial responder; or peginterferon/RBV Treatment Relapse * For human immunodeficiency virus (HIV) co-infected participants: documented HIV-1 infection; currently naïve to treatment with any antiretroviral therapy (ART) and have no plans to initiate ART treatment while participating in this study; or be on HIV ART for at least 8 weeks prior to study entry (dual nucleoside reverse transcriptase inhibitor \[NRTI\] backbone of tenofovir or abacavir and either emtricitabine or lamivudine plus raltegravir (or dolutegravir or rilpivirine) (no changes in HIV regimen allowed within 4 weeks of randomization); cluster of differentiation 4 (CD4)+ T-cell count \>200 cells/mm\^3 at screening; documented undetectable plasma HIV-1 RNA at least 8 weeks prior to screening; participants not on ART, HIV RNA must be \<50,000 copies/mL; must have at least one viable antiretroviral regimen alternative beyond their current regimen in the event of HIV virologic failure and the development of antiretroviral drug resistance * Agree to use two acceptable methods of birth control from at least 2 weeks prior to Day 1 and continue until at least 6 months after last dose of study drug, or longer if dictated by local regulations; a male participant who is not (or whose partner is not) of reproductive potential is eligible without requiring the use of contraception Exclusion Criteria: * Evidence of decompensated liver disease manifested by the presence of or history of ascites, esophageal or gastric variceal bleeding, hepatic encephalopathy or other signs or symptoms of advanced liver disease * For participants with cirrhosis, participants who are Child-Pugh Class B or C or who have a Pugh-Turcotte (CPT) score \>6, must be excluded * Co-infected with hepatitis B virus * Has had previous direct-acting antiviral treatment * History of malignancy \<=5 years prior except for adequately treated basal cell or squamous cell skin cancer or in situ cervical cancer or carcinoma in situ; or is under evaluation for other active or suspected malignancy * Has cirrhosis and liver imaging showing evidence of hepatocellular carcinoma (HCC) or is under evaluation for HCC * Taking or plans to take any HIV therapy that includes a ritonavir-boosted or unboosted protease inhibitor, efavirenz or etravirine * Currently participating or has participated in a study with an investigational compound within 30 days of signing informed consent and is not willing to refrain from participating in another such study during the course of this study * Clinically-relevant drug or alcohol abuse within 12 months * Pregnant, breast-feeding, or expecting to conceive or donate eggs or sperm from Day 1 and continue until at least 6 months after last dose of study drug, or longer if dictated by local regulations; or is a male whose female partner(s) is/are pregnant * History of organ transplant (including hematopoietic stem cell transplants) other than cornea and hair * Poor venous access * History of gastric surgery (e.g., stapling, bypass) or history of malabsorption disorders (e.g., celiac sprue disease) * Hemoglobinopathy, including, but not limited to, thalassemia major * Any medical condition requiring, or likely to require, chronic systemic corticosteroids, tumor necrosis factor (TNF) antagonists, or other immunosuppressant drugs during the course of the trial * For participants with HIV, history of opportunistic infection in the preceding 6 months * For participants with HIV, use of HIV drugs other than a dual NRTI backbone of tenofovir or abacavir and either emtricitabine or lamivudine plus raltegravir (or dolutegravir or rilpivirine) * Evidence or history of chronic hepatitis not caused by HCV, including but not limited to nonalcoholic steatohepatitis (NASH), drug-induced hepatitis, and autoimmune hepatitis