A Pharmacokinetics (PK) and Safety Study to Determine the Effect of Repeat Dosing of Trametinib on Combined Oral Contraceptive (Norethindrone Plus Ethinyl Estradiol) in Female Subjects With Solid Tumors

Inclusion Criteria: * Is a female subject \>=18 years but \<59 years of age at the time of signing the informed consent. * Has a histologically or cytologically confirmed diagnosis of a solid tumor malignancy (except for any excluded malignancies listed in Exclusion Criteria) that is not responsive to standard therapy(ies) or for which there is no approved therapy. * Is capable of giving written informed consent, which includes compliance with the requirements and restrictions listed in the informed consent form (ICF). * Has an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Has a body mass index (BMI) within the range of 19 to 40 kilogram/squared meter (kg/m\^2) (inclusive) * Is a non-smoker or is willing to abstain from use of tobacco and/or nicotine-containing products from time of Screening until the post-treatment follow-up visit or transition to MEK rollover study (MEK114375). * Meets one of the following criteria: Is currently on a stable regimen of ORTHO-NOVUM® tablet 1/35, or Is willing to switch to a regimen of ORTHO-NOVUM® tablet 1/35 from a stable regimen of an alternate OC, or Is willing to start a regimen of ORTHO-NOVUM® tablet 1/35 * Has a negative serum beta-human chorionic gonadotropin (Beta-hCG) pregnancy test within 7 days of first dose of study treatment * Meets one of the following criteria: Is of non-childbearing potential - defined as females with a documented bilateral tubal ligation or tubal occlusion or hysterectomy without oophorectomy (at least one functioning ovary required); Is of childbearing potential and agrees to use an appropriate method of contraception in addition to the OC provided for at least 14 days prior to the first dose of study treatment until completion of the post-treatment follow-up visit or transition to the Mitogen-activated extracellular signal-regulated kinase (MEK) rollover study (MEK114375) * Has no prior treatment- related toxicities \>Grade 1 (except alopecia) at the time of enrollment * Is able to swallow and retain orally administered medication * Has adequate baseline organ function as follows: Hematologic (Absolute neutrophil count \>=1.2 × 10\^9/L; Hemoglobin \>=9 g/dL; Platelets \>=75 × 10\^9/L; prothrombin time/international normalized ratio \[PT/INR\] and partial thromboplastin time \[PTT\] \<=1.5x upper limit of normal \[ULN\]) ; Hepatic (Albumin \>=2.5 g/dL; Total bilirubin \<=1.5xULN \[isolated bilirubin \>1.5x ULN is acceptable if bilirubin is fractionated and direct bilirubin \<35%\]); alanine aminotransferase (ALT) \<=2.5xULN; ALT with documented liver metastases or tumor infiltration; \>2.5xULN but \<=5xULN) ; Renal (Creatinine or \<=1.5 ULN; Calculated creatinine clearance \[calculated by the Cockcroft-Gault formula\] \>=50 milliliters/minute \[mL/min\]) ; Cardiac (left ventricular ejection fraction \[LVEF\] \>= lower limit of normal \[LLN\] by echocardiogram \[ECHO\] or Multigated acquisition scan \[MUGA\]) Exclusion Criteria: A subject will not be eligible for inclusion in this study if any of the following criteria apply: * Had prior exposure to a MEK inhibitor * Has one of the following excluded tumor types as trametinib therapy has been shown to have minimal benefit in these populations: BRAF V600E mutant melanoma and failed prior BRAF inhibitor therapy; Metastatic pancreatic cancer * Has had any major surgery extensive radiotherapy, or anti-cancer therapy (e.g., chemotherapy with delayed toxicity, biologic therapy, or immunotherapy) within 21 days prior to enrollment and/or daily or weekly chemotherapy without the potential for delayed toxicity within 14 days prior to enrollment. Prolonged immobilization must have resolved prior to start of study. * Has a known or suspected carcinoma listed below that is excluded as administration of ORTHO-NOVUM® tablet would be contraindicated: carcinoma of the breast, or carcinoma of the endometrium, or BRCA+ ovarian cancer, or other known or suspected estrogen-dependent neoplasia, or hepatocellular carcinoma * Has a history of another malignancy: Exception: A subject who: has been disease-free for 3 years, or; has a history of completely resected non-melanoma skin cancer, or; has an indolent second malignancy, other than any of the excluded malignancies listed in the previous exclusion Criteria. * Has a life expectancy of \<3 months * Has a history of interstitial lung disease or pneumonitis. * Has a history of Retinal vein occlusion (RVO) * Has a history of any of the following conditions that would contraindicate administration of an Oral contraceptive (OC): Uncontrolled or treatment refractory hypertension. NOTE: Treatment-refractory hypertension is defined as a blood pressure of systolic \>140 millimeters of mercury (mmHg) and/or diastolic \>90 mmHg which cannot be controlled by anti-hypertensive therapy; Diabetes mellitus (type 1 and 2) with vascular involvement (neuropathy./retinopathy/nephropathy); Stroke; Acute or past history of venous thromboembolism or known thrombophilia including factor V Leiden mutation; prothrombin mutation; protein S, protein C, and antithrombin deficiencies; or antiphospholipid antibodies; Migraine headaches (headaches with focal neurological symptoms); Undiagnosed abnormal uterine bleeding * Has a Bazett-corrected QT (QTcB) interval \>=480 milliseconds (msec) at Screening * Has a LVEF, as measured by ECHO (preferred) or MUGA scan, below the institutional LLN, or if a LLN does not exist at an institution, \<50% * Has a history or current evidence of cardiovascular risk including any of the following: History or evidence of current clinically significant uncontrolled arrhythmias. NOTE: Subjects with controlled atrial fibrillation for \>30 days prior to enrollment are eligible. History or evidence of current acute coronary syndromes (including myocardial infarction and unstable angina), coronary angioplasty, or stenting within 6 months prior to enrolment. History or evidence of current \>=Class II congestive heart failure as defined by New York Heart Association (NYHA); Has an intra-cardiac defibrillator * Has symptomatic or untreated leptomeningeal, brain metastases, or spinal cord compression. Note: Subjects previously treated for these conditions that have had stable central nervous system disease (verified with consecutive imaging studies) for \>3 months, are asymptomatic and are not currently taking corticosteroids, or are on stable dose of corticosteroids for at least 30 days prior to Day 1 are permitted. * Has any clinically significant gastrointestinal (GI) abnormalities that may alter absorption such as malabsorption syndrome or major resection of the stomach or bowels. * Is pregnant, lactating or actively breastfeeding. * Is currently receiving a prohibited medication(s) or requires the use of any of the prohibited medication(s) during the study. NOTE: Use of anticoagulants such as warfarin is permitted; however, INR must be monitored in accordance with local institutional practice. * Presence of hepatitis B surface antigen (HBsAg) or positive hepatitis C antibody at Screening or within 3 months prior to first dose of study treatment . NOTE: Subjects with laboratory evidence of cleared hepatitis B virus and hepatitis C virus infection will be permitted. * Has current or chronic history of liver disease or known hepatic or biliary abnormality (with the exception of Gilbert's syndrome or asymptomatic gallstones, liver metastases or otherwise stable chronic liver disease per investigator assessment ). NOTE: Stable chronic liver disease defined by the absence of ascites, encephalopathy, coagulopathy, hypoalbuminemia, oesophageal or gastric varices, or persistent jaundice. * Has participated in a clinical trial and received investigational drug(s) within 30 days, 5 half-lives or twice the duration of the biological effect of trametinib whichever is longer, prior to enrollment in this study. * Has participated in a study that resulted in or made a donation of blood or blood products in excess of 500 mL within 56 days of the first dose of study treatment. * Has a known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to study treatment, or excipients. * Has any serious and/or unstable pre-existing medical disorder (aside from malignancy exception above), psychiatric disorder, or other conditions that could interfere with subject's safety, obtaining informed consent or compliance to the study procedures