Functions

Question

1)How many injective function are there which are also bijective with n elements?

2)How many injective function of n elements are there among which m elements are also bijective  ?

3)How many onto function of n elements are there among which m elements are also bijective  ?

4)How many injective function of n elements are there among which m elements are also surjective  ?

Comments

@srestha mam

questions need to be some more clarity... otherwise you can give sample examples with small no.of elements

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see this https://gateoverflow.in/82437/gate1987-9b

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did you mean

let | A | = n and | B | = m

1) Howmany functions from A to A which are bi-jective

2) Howmany functions from A to B which are bi-jective

​​​​3) Howmany functions from A to B which are bi-jective

4) Howmany functions from A to B which are bi-jective

note that 2,3 and 4 are equal.

for all this questions n! is the answer, but note that m should be equal to n for 2,3,4 due to it is necessary condition for bijection