Your first sentence is fine. You could also simply say "a scholarship to Oxford", since "to study" is implicit.
Your second sentence is also fine, but is ambiguous; it can mean:
1. Very few people can win a scholarship to Yale.
2. Very few people, once they win a scholarship, can successfully complete their studies at Yale.
3. I would guess that there are very few scholars at Yale.
(Some of these statements are more controversial than others.)
All the best,
Not a professional ESL teacher.