Counting functions problem 4

Could someone please check my answers for the following problems, especially b?

Consider the possible functions f:[7] [9]?

a) How many have f(3)=8? How many have f(3) 8?

There is one object being distributed to one recipient for f(3)=8, plus 6 objects being distributed to 9 recipients. So there are possible functions that have f(3)=8. For the second part of the question, has 8 different functions plus 6 objects being distributed to 9 recipients. So there are possible functions that have .

b) How many have and are one-to-one?

In this case we have 8 possible functions for plus .

c) How many have even for all i?

There are 4 even numbers in the Codomain, which gives distributions of 7 objects to 4 recipients.

d) How many have ?

That would be 7 objects distributed to 2 recipients, so .

e) How many in which is not a function?

This would be the same as the total number of distributions of 7 objects to 9 recipients minus the number which have a one-to-one relationship which would be .So the answer is .