Combinatorics
2014
The doctor gave Amber ten vitamins, with instructions to take one or two each day until she runs out of vitamins. For example, Amber could take a vitamin a
day for ten days, or she could take two the first day and one a day for the next eight days. A third way is to take one vitamin a day for eight days and two on the ninth day. Including the three examples given, in how many different ways can Amber take the ten vitamins?