Problem 1: Bill is buying his wife a bouquet of carnations, daises, roses and tulips. The bouquet will have 26 flowers, with
• between 2 and 11 carnations,
• at most 6 daises,
• at least 3 roses, and
• between 3 and 9 tulips.
How many different combinations of flowers satisfy these requirements? You need to use the counting method for integer partitions and show your work.