If$A=\left\{a_1,a_2,a_3,...,a_{10}\right\}$ and$B=\left\{b_1,b_2,b_3,...,b_{10}\right\}$ then the number of bijections that can be defined from A to B is 

The given sets are $A=\left\{a_1,a_2,a_3,...,a_{10}\right\}$ and $B=\left\{b_1,b_2,b_3,...,b_{10}\right\}$

Both have same number of elements $n\left(A\right)=n\left(B\right)=10$

The number of bijective functions from  $A$ to $B$ is $n\left(A\right)!$ where $n\left(A\right)=n\left(B\right)$

Therefore the number of bijecitve functions from the set $A$ to the set $B$ is $\boxed{10!}$