Explain how we can find number of bijective functions from set A to set B if n(A)=n(B).

Asked by abhinavsaini123 | 1st Jun, 2015, 09:00: PM

Expert Answer:

If a function defined from set A to set B f:A->B is bijective, that is one-one and and onto, then n(A)=n(B)=n
So first element of set A can be related to any of the 'n' elements in set B.
Once the first is related, the second can be related to any of the remaining 'n-1' elements in set B.
If we proceed like this , the total number of ways of relating every element of set A to a unique element of set B can be found by using multiplication principle of counting,
n(n-1)(n-2)(n-3)....2X1= n!

Answered by satyajit samal | 3rd Jun, 2015, 09:10: AM

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