In the Dutch General Election, 1948, the largest party was KVP with 32 seats. Second was PvdA with 27 seats. Normally the largest party provides the prime minister. Yet in the folowing KVP-PvdA-CHU-VVD coalition government, the prime minister was Drees (PvdA) rather than Van Schaik (KVP). Why did the second largest party rather than the largest party provide the prime minister between 1948 and 1951?
In Dutch politics the prime minister and his cabinet are formed through negotiations between a number of political parties. Which posts are provided by which party (ordered by size or whatever) is not automatic.
I don't know what determined the distribution in this cabinet, but quite likely the choice of prime minister was determined by who was most acceptable to all parties involved in order to lead to the most stable coalition government. It's also possible the KVP had the best financial expert, and was therefore given the ministry of finance, the finance minister typically being the deputy prime minister that would then logically lead to the second largest party providing the prime minister (it's normal in Dutch cabinets that the PM and finance minister are provided by the 2 largest parties, but not by the same party).
Also remember that the cabinet is not decided solely by the parties involved. The person in charge of negotiating the cabinet is appointed by the ruling monarch, not parliament. Though often an elder statesman and/or senior member of parliament (and often of the largest party) this isn't guaranteed. The ruling monarch also has final say over whether the negotiated cabinet is acceptable and can take office, and some monarchs have been known to require their personal political ideas to influence the composition of the cabinet (and the Dutch royal family are Dutch Reformists, the KVP is Roman Catholic, so the Queen may have intervened in the choice of prime minister).