Question

Claudette has a selection of caffeinated teas at home: 3 kinds of Assam, 6 kinds of Earl Grey, and 4 kinds of breakfast blends. She has enough of each that she could drink each one every morning for a week and not run out. She (and whoever stays with her) has a single cup of caffeinated tea every morning. (a) How many different sequences of types of cups of tea could Claudette have over the course of a week? 1 (b) If Claudette decides to drink each kind of tea no more than once within a week, how many different sequences of types of cups of tea could she have in that week? (c) Now suppose Claudette’s friend Bobby visits for thirteen days and they drink a different kind of tea each morning (in other words, each kind of tea will be drunk, and drunk exactly once). Bobby doesn’t drink much tea and can’t tell the difference between the different Assams, the different Earl Greys, and the different blends. How many different sequences of cups of tea over the course of the thirteen days could Bobby distinguish?

Answer 1