You do not need an entry for each dimension combination.
Typically a fact table (or cube) will be very small compared to the theoritical size (i.e., the multiplication of the dimension's cardinalities). This theoritical number of rows (or cells) can be very very large even with a relative small number of dimensions (e.g., time, products, geography, customers, sales, etc...). This is known as cube's sparsity; OLAP engines (e.g., icCube, SSAS, etc...) are typically built to handle efficiently this sparsity.