Option C is correct
choose k element from n element of set S =nCk
now set A have k element so match this k element to the choose nCk element=nCk*k!
now set B have k element so match this k element to the choose nCk element= nCk*k! (k!) (because each matching of function nCk *k! will from k! with B)
means black color function is nCk*k! and each this function form k! matching with b
watch i formed two matching ,one with yellow color and one with gray color from B to black function (total K! try to made in mind) ,similarly from every black matching we can form k! matching
after doing this same thing will be done with C also
so nCk*k!*k!*k!