This study has two stages. In the erlotinib group, the combination treatment will be given to participants with epidermal growth factor receptor (EGFR) tyrosine kinase inhibitor (TKI)-treatment-naive, advanced (nonresectable) NSCLC in a safety-evaluation stage and to participants with previously untreated EGFR mutation-positive, advanced NSCLC in an expansion stage (Stage 2). In the alectinib group, for both the safety-evaluation and expansion stages (Stages 1 and 2), the combination will be given to participants who are treatment-naive with anaplastic lymphoma kinase (ALK)-positive advanced NSCLC.