(1) Cody has a selection of caffeinated teas at home: 3 kinds of Assam, 6 kinds

Question

(1) Cody has a selection of caffeinated teas at home: 3 kinds of Assam, 6 kinds of Earl Grey, and 4 kinds of breakfast blends. He has enough of each that he could drink each one every morning for a week and not run out. He (and whoever stays with him) has a single cup of caffeinated tea every morning.

(a) How many different sequences of types of cups of tea could Cody have over the course of a week?

(b) If Cody 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 he have in that week?

(c) Now suppose Cody'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?

Explanation / Answer

a)

for there are 13 choice for each day ; hence total number of different sequence =137 =62748517

b)

P(for no kind of tea can be again used ; hence total number of different sequence =13*12*11*10*9*8*7

=8648640

c)

here as Bobby can not distinguish ; number of ways to arrange 3 Assam; 6 Earl grey adn 4 breakfast blends =13!/(3!*6!*4!) =60060

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