Math, asked by murthy20, 11 months ago

Let n(A) = 4 and n(B)=k. The number of all possible injections from A to B is 120. then k=​

Answers

Answered by Anonymous
37

k = 5

  • It is given that n(A) = 4 and n(B) = k.
  • Now an injection is a bijection onto its image. Thus we can find the number of injections by counting the possible images and multiplying by the number of bijections to said image.
  • Now the number of bijections is given by p!, in which p denotes the common cardinality of the given sets.
  • So the required number is (\left { {{q} \atop {p}} \right. )*p! where n(A) = p and n(B) = q.
  • Here p = 4 and q = k.
  • Now (\left { {{k} \atop {4}} \right. )*4! = 120
  • this implies (\left { {{k} \atop {4}} \right. ) = 5 or k = 5
  • Hence the value of k is 5.
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