More generally, one can count points of Grassmannian over F: in other words the number of subspaces of a given dimension k. This requires only finding the order of the stabilizer subgroup of one such subspace and dividing into the formula just given, by the orbit-stabilizer theorem.
morE gEnerally One can couNt poInts of grassManNian oVer f in otHer worDS the NumbEr of SubSpAceS of a giVen DImenSion k thiS rEquiRes only findINg tHE OrDEr of the STabilIZEr SubgrOUP of onE such SubspAce aND dividing inTo the foRMula just GIven by ThE orbiT-stabiliZeR tHeoREM