The purpose of the paper is to provide an answer to a long standing problem to compute the distance distribution among the nodes in a star graph, i.e., to compute the exact number of nodes at a distance k from the identity node in a star graph where k varies from 0 to the diameter of the graph. A star graph is a Cayley graph like the hypercubes; for a hypercube Qn, there are exactly `n r´ nodes at a distance r from the identity node where r varies from 0 to n.