How many triples of positive integers (a,b,c) are there such that a!+b3=18+c3?<spanclass=′latex−bold′>(A)</span> 4<spanclass=′latex−bold′>(B)</span> 3<spanclass=′latex−bold′>(C)</span> 2<spanclass=′latex−bold′>(D)</span> 1<spanclass=′latex−bold′>(E)</span> 0 geometry3D geometrymodular arithmetic