According to me, the answer should be n! m(m-1) / 2* (n-m+1)! (m-2)!
as selecting any 2 elements from “m”= mC2 and selecting any element from “n” for its mapping= nC1
so we get mC2 *nC1 ----(1)
now for the remaining “m-2” elements in “m” we can select them from “n-1” for mapping as n-1Cm-2 -----(2)
combining both (1) and (2)
(mC2) (nC1) (n-1Cm-2) which should be the above one as mentioned.