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Let A,B,C are k element sets and let S be an n element set where k<= n. How many triples of functions f: A→ S , g: B → S , h: C → S are there such that f,g,h are all injective and f(A) = g(B) = h(C)

  1. 3.P(n,k) . k!
  2. P(n,k).(k!)$^{3}$
  3. C(n,k).(k!)$^{3}$ 
  4. 3.C(n,k).k!
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Which of them is valid ? How to solve it?