JNU 20182 PhD CS
October 26, 2023ComputerGraphics
October 26, 2023JNU 20182 PhD CS
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 onetoone functions is
^{n}C_{m} × m!


^{n}C_{m} × n!


^{m}C_{n} × m!


^{m}C_{n} × n!

Question 23 Explanation:
For the function f to be oneone 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 onetoone function will be ^{n}C_{m} × m!, because we will select m elements from set B which will have ^{n}C_{m} 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 oneto one functions possible is ^{n}C_{m} × m!.
Correct Answer: A
Question 23 Explanation:
For the function f to be oneone 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 onetoone function will be ^{n}C_{m} × m!, because we will select m elements from set B which will have ^{n}C_{m} 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 oneto one functions possible is ^{n}C_{m} × m!.
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