If set A has cardinality = n
If set B has cardinality = m
then No of one to one function from A to B are = mPn
According to given data in question.
If set A has cardinality = 9
If set B has cardinality = n
hence the No of One to one function from A to B are = nP9
Explanation :-
starting from ele 1 of set A no of choices = n
ele 2 of set A no of choices = n-1
ele 3 of set A no of choices = n-2
ele 4 of set A no of choices = n-3
ele 5 of set A no of choices = n-4
ele 6 of set A no of choices = n-5
ele 7 of set A no of choices = n-6
ele 8 of set A no of choices = n-7
ele 9 of set A no of choices = n-8
hence total no of one to one function are
n * (n-1) * (n-2) * (n-3) * (n-4)* (n-5)* (n-6)* (n-7)* (n-8)
which is in short equal to nP9