JNU 2018-2 PhD CS
October 26, 2023UGC NET CS 2014 Dec – paper-3
October 26, 2023JNU 2018-2 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 one-to-one functions is
| nCm × m! | |
| nCm × n! | |
| mCn × m! | |
| 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!.
Correct Answer: A
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!.
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