Question

There are six ways to write 5 as an ordered sum of three positive integers: 3+1+1, 1+3+1, 1+1+3, 2+2+1, 2+1+2, 1+2+2.
A) What is the number of ways to write "n" as an ordered sum of "r" integers?
B) What is the number of ways to write "n" as an ordered sum of positive integers? For example, when n=3 the answer is four: 3, 1+2, 2+1, 1+1+1