Isomorphism and Subgraphs · Challenge problem

Label the Petersen graph by an outer $5$-cycle $o_0,\ldots,o_4$, inner pentagram $i_k\sim i_{k+2}$, spokes $o_ki_k$. How many $4$-element subsets of the Petersen graph's $10$ vertices form an independent set (no two of the $4$ are adjacent)?