This is a 5-part dose-finding and preliminary efficacy study of pembrolizumab (Pembro) + dabrafenib (D) + trametinib (T) for participants with advanced melanoma. Parts 1 and 2 are open-label to find and confirm the maximum tolerated dose (MTD)/maximum administered dose (MAD) for Pembro+D+T. The primary hypothesis (Parts 1 and 2) is that Pembro+D+T is sufficiently well-tolerated to permit clinical investigation. Part 3 is a double-blind study of Pembro+D+T versus placebo+D+T. The primary study hypothesis (Part 3 only) is that the Pembro+D+T improves progression-free survival (PFS) compared with placebo+D+T. Part 4 is nonrandomized and open-label and is designed to evaluate the safety and tolerability and identify the MTD or MAD of Pembro+T in participants who have v-raf murine sarcoma viral oncogene homolog B1 [BRAF] mutation-negative (without V600 E or K) melanoma or solid tumors [irrespective of BRAF status]. The primary hypothesis (Part 4) is that Pembro+T is sufficiently well-tolerated to permit clinical investigation. Part 5 will confirm the dose(s) identified in Part 4 in participants BRAF wild type [without V600E or K] melanoma or solid tumors [irrespective of BRAF status] and will further evaluate the safety and preliminary efficacy (Objective Response Rate [ORR]) of Pembro+T in participants who have BRAF wild type [without V600E or K] melanoma only. The primary hypotheses (Part 5) are that Pembro+T is sufficiently well-tolerated at the MTD/MAD to permit further clinical investigation and is effective in attaining objective responses based upon Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1 by Investigator review in participants who have melanoma without BRAF V600 E or K mutations.