October 26, 2023
October 26, 2023
October 26, 2023
###### Computer-Graphics
October 26, 2023
 Question 23
A function f is defined from set A to set B. A and B have m and n (m≤n) elements, respectively. Then the number of one-to-one functions is
 A nCm × m! B nCm × n! C mCn × m! D mCn × n!
Question 23 Explanation:
For the function f to be one-one no. of elements in A must be less than or equal to B. And yes it is given that m<=n. So the no. of one-to-one function will be nCm × m!, because we will select m elements from set B which will have nCm ways and then each elements from selected elements of B can be mapped to one elements each in A which will have m! Ways and therefore making total no. of one-to one functions possible is nCm × m!.
Question 23 Explanation:
For the function f to be one-one no. of elements in A must be less than or equal to B. And yes it is given that m<=n. So the no. of one-to-one function will be nCm × m!, because we will select m elements from set B which will have nCm ways and then each elements from selected elements of B can be mapped to one elements each in A which will have m! Ways and therefore making total no. of one-to one functions possible is nCm × m!.