I have problem with this questions:

How many different 5-element subsets can be formed from the set {1,2,3,4,5,6,7,8,9}? Two elements of the original set are said to form S-pair if their sum is equal to 10. Show that every 5-element subset that does not contain an S-pair must contain 5. How many subsets will not contain any S-pairs? Give a list of all such subsets.

[Hint:using pigeon hole principle and inclusion-exclusion principle].

Can anybody help!!!