Efficacy and Safety Study of Fosaprepitant (MK-0517) Plus Ondansetron Versus Ondansetron Alone for the Prevention of Chemotherapy-Induced Nausea and Vomiting in Pediatric Participants (MK-0517-044)

Inclusion Criteria: * Is 0 (at least 37 weeks gestation) to 17 years of age at time of randomization * Has a Lansky Play Performance score ≥60 (participants ≤16 years of age) or a Karnofsky score ≥60 (participants \>16 years of age) * Has a predicted life expectancy ≥3 months * Is receiving chemotherapeutic agent(s) associated with moderate or high risk of emetogenicity, or a chemotherapy regimen not previously tolerated due to vomiting * Has a preexisting functional central venous catheter available for study drug administration * Is male OR is female who is not of reproductive potential OR is female who is of reproductive potential and agrees to avoid becoming pregnant in the 28 days prior to receiving study drug, while receiving study drug and for at least 30 days after last dose of study drug Exclusion Criteria: * Has vomited in the 24 hours prior to chemotherapy initiation on Treatment Day 1 * Has a symptomatic primary or metastatic central nervous system (CNS) malignancy with nausea and/or vomiting (asymptomatic participants may participate in study) * Will be receiving stem cell rescue therapy in conjunction with study-related course of emetogenic chemotherapy or during the 14 days following administration of fosaprepitant/placebo for fosaprepitant * Has received or will receive total body irradiation of radiation therapy to the abdomen or pelvis in the week prior to Treatment Day 1 and/or during the diary reporting period (120 hours following initiation of chemotherapy) * Has had benzodiazepine, opioid or opioid like therapy initiated within 48 hours prior to study drug administration, or is expected to receive within 120 hours following initiation of chemotherapy except for single doses of midazolam, temazepam or triazolam * Has started on systemic corticosteroid therapy within 72 hours prior to study drug administration or is expected to receive a corticosteroid as part of the chemotherapy regimen * Is currently taking, or has taken within 48 hours of Treatment Day 1 the following drugs with antiemetic properties: 5-hydroxytryptamine 3 (5-HT3) antagonists (e.g., ondansetron), benzamides (e.g., haloperidol), cyclizine, domperidone, herbal therapies with potential antiemetic properties, olanzapine, phenothiazines (e.g., prochlorpenzine), scopolamine (this is not an exhaustive list) * Is or has an immediate family member who is investigational site or sponsor staff directly involved with this study * Is currently a user of any recreational or illicit drugs (including marijuana) or has current evidence of drug or alcohol abuse or dependence * Is mentally incapacitated or has a significant emotional or psychiatric disorder * Is pregnant or breast feeding * Is allergic to fosaprepitant, aprepitant (MK-0869), ondansetron, or any other 5-HT3 antagonist * Has a known history of QT prolongation or is taking any medication that is known to lead to QT prolongation * Has an active infection (e.g., pneumonia), congestive heart failure, bradyarrhythmia, any uncontrolled disease (e.g., diabetic ketoacidosis, gastrointestinal obstruction) except for malignancy * Has ever participated in a previous study of aprepitant or fosaprepitant or has taken an investigational drug with the last 4 weeks.