Question

if n(a) = p then number of bijective functions from set a to a are​

Answer 1

Answer:

For a finite set S, there is a bijection between the set of possible total orderings of the elements and the set of bijections from S to S. That is to say, the number of permutations of elements of S is the same as the number of total orderings of that set, i.e. n!. 

We have the set A that contains 106 elements, so the number of bijective functions from set A to itself is 106!.

Answer 2

p!

Bijective functions are those which are one-one and onto as well.

Bijective function will contain all the ordered pairs from the given set of elements.

For example if a set contains two elements that is {a,b}

then bijective function will be same as all the ordered pairs that is { (a,b) , (b,a) }

hence there will be 2 bijective functions that is 2!

so we can say that if a set contains p elements then number of bijective functions will be p!.