Answer
a) 0
b) 120
c) 720
d) 2520
Work Step by Step
a) It will not be a function as an item from the domain will not linked with another item from the codomain.
b) we have 5 items in the codomain set to choose from and 5 items in the domain set to choose for them ( the number of choices)
Now, by using permutation 5P5 =120 possible functions.
c) we have 6 items in the codomain set to choose from and 5 items in the domain set to choose for them ( the number of choices)
Now, by using permutation 6P5 =720 possible functions.
d) we have 7 items in the codomain set to choose from and 5 items in the domain set to choose for them ( the number of choices)
Now, by using permutation 7P5 =2520 possible functions.
You can see an another solution below (it will show the same concept but in another way of counting technique).
