Question

No of one to one function from set A={1,2,3,4,5,6,7,8,9} to set B ={x1,x2,x3,x4,x5,x6,x7,.....,xn}

Answer 1

If set A has cardinality = n

If set B has cardinality = m 

then No of one to one function from A to B are  = ^mP_n 

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