Question

Find the number of bijective functions from set A to itself when A contains 106 elements.

• A. $106$
• B. ${106}^2$
• C. $106!$
• D. $2^{106}$

Answer 1

The correct option is C $106!$

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 $106!$.