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Please explain

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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!


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