SOLUTION: In how many ways can 10 different books be divided a and b so that one gets 6 books and the other 4 books?

This is the same as asking "In how many ways can you choose 4 books out of a set
of 10 books?" Because once you choose a set of 4, the other set is automatically 
6.

So the number of ways is C(10,4) (which is also equal to C(10,6) since C(N,n) 
is the same as C(N,N-n))

=  = 210 ways.

:)