Let n(A) = 4 and n(B)=k. The number of all possible injections from A to B is 120. then k=
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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 where n(A) = p and n(B) = q.
- Here p = 4 and q = k.
- Now
- this implies or k = 5
- Hence the value of k is 5.
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