A Study of the Effect of Dulaglutide on How the Body Handles Oral Contraceptive in Healthy Female Participants

Inclusion Criteria: * Are females of child-bearing potential, and who are overtly healthy as determined by medical history and physical examination * As it is possible that dulaglutide may cause the oral contraceptive (OC) tablet to be less effective than usual, participants will be required to use 2 additional highly effective methods of contraception from the screening appointment until 2 months after the poststudy follow-up appointment. Additional methods of contraception may include the following: a non-hormonal intrauterine device with spermicide; male or female condom with spermicide; contraceptive sponge with spermicide; diaphragm with spermicide; cervical cap with spermicide; sterile sexual partner; or abstinence (participants reporting abstinence who become sexually active while on the study must agree to use other additional methods of contraception). The pregnancy test result must be negative at screening and at each check-in * Have a body mass index (BMI) of between 18.5 and 30.0 kilogram-meter squared (kg/m\^2), at screening * Have no clinically significant findings, as determined by the investigator, upon bimanual pelvic and breast examinations, at screening (provision of previous gynecological examination documentation may be accepted) * Have clinical laboratory test results within the normal reference range for the population or investigator site, or results with acceptable deviations that are judged to be not clinically significant by the investigator * Have venous access sufficient to allow for blood sampling * Are reliable and willing to make themselves available for the duration of the study and are willing to follow study procedures and restrictions * Have given written informed consent approved by Lilly and the ethical review board (ERB) governing the site Exclusion Criteria: * Are currently enrolled in, have completed or discontinued within the last 30 days from, a clinical trial involving an investigational product, or are concurrently enrolled in any other type of medical research judged not to be scientifically or medically compatible with this study * Have known allergies to Ortho-Cyclen, dulaglutide, or to related compounds or to any components of either formulation * Are persons who have previously completed or withdrawn from this study or any other study investigating dulaglutide within 3 months prior to screening or have received glucagon-like peptides or incretin mimetics in the 3 months prior to screening * Have an abnormality in the 12-lead electrocardiogram (ECG) that, in the opinion of the investigator, increases the risks associated with participating in the study * Have an abnormal blood pressure (BP) (after at least 5 minutes sitting) that, in the opinion of the investigator, increases the risks associated with participating in the study * Have a history or presence of respiratory, hepatic, renal, endocrine, hematological, or neurological disorders capable of significantly altering the absorption, metabolism, or elimination of drugs; of constituting a risk when taking the study medication; or of interfering with the interpretation of data * Have a history or presence of cardiovascular disorder (including myocardial infarction, cerebrovascular accident, coronary artery disease, venous thromboembolism, arrhythmia \[judged by the investigator to be clinically significant\], or angina) within the last year, have symptoms or signs of congestive heart failure, or are expected to require coronary artery bypass surgery or angioplasty * Have a history or presence of pancreatitis (history of chronic pancreatitis or idiopathic acute pancreatitis) or gastrointestinal disorder, for example relevant esophageal reflux or gall bladder disease, or any gastrointestinal disease which impacts gastric emptying (GE) (such as, gastric bypass surgery, pyloric stenosis, with the exception of appendectomy) or could be aggravated by glucagon-like-peptide 1 (GLP-1) analogs. Participants with dyslipidemia, and participants who had cholecystolithiasis (removal of gall stones) and/or cholecystectomy (removal of gall bladder) in the past, with no further sequelae, may be included in the study at the discretion of the screening physician * Show evidence of significant active neuropsychiatric disease * Have family history of medullary thyroid cancer (MTC) or a genetic condition that predisposes to MTC * Regularly use known drugs of abuse and/or show positive findings on urinary drug screening * Show evidence of human immunodeficiency virus (HIV) infection and/or positive HIV antibodies * Show evidence of hepatitis C and/or positive hepatitis C antibody * Show evidence of hepatitis B and/or positive hepatitis B surface antigen * Are women with a positive pregnancy test or women who are lactating * Have used or intend to use St John's Wort within 21 days of study drug administration or are unable/unwilling to adhere to the study drug restrictions * Have donated blood of more than 500 milliliter (mL) within the last month prior to admission of the lead-in phase * Have an average weekly alcohol intake that exceeds 14 units per week, or are unwilling to stop alcohol consumption for 48 hours prior to each admission to the clinical research unit (CRU) and while resident at the CRU (1 unit = 12 ounce \[oz\] or 360 mL of beer; 5 oz or 150 mL of wine; 1.5 oz or 45 mL of distilled spirits) * Use of any tobacco- or nicotine-containing products (including but not limited to cigarettes, pipes, cigars, chewing tobacco, nicotine patches, nicotine lozenges, or nicotine gum) within 6 months prior to admission into the lead-in phase * Have taken injectable contraceptives or have used hormonal implants within 12 months of enrollment to this study or topical controlled delivery contraceptives (patch) or hormonal intrauterine devices (such as, Mirena® device) within 3 months prior to enrollment of this study * The history or presence of any contraindications to the combined OC tablet including thrombosis and a history of thromboembolic disease, recurrent jaundice, acute or chronic liver disease, migraines, undiagnosed vaginal bleeding, significant hyperlipidemia, hepatic adenoma, and mammary, endometrial, or hepatic carcinoma or any other estrogen-dependent neoplasia (known or suspected) * In the opinion of the investigator or sponsor, are unsuitable for inclusion in the study