Question

There are eight people in your group at the basketball game, and they ask you to go and get a cold drink for everyone. Assuming everyone orders one of Kooky cola, Pixy cola, or Dr PhD, how many drink orders are possible?

Answer 1

Hi,

45

Explanation:

Let's find the number of Kooky, of Pixy cola, of Dr PhD (in that order)

It is the number of drink to order to the waiter.

(0,0,8) (0,1,7),(0,2,6),...,(0,7,1),(0,8,0) : 9 cases

(1,0,7),(1,1,6),(1,2,5),(1,3,4),(1,4,3),(1,5,2),(1,6,1),(1,7,0) :8 cases

(2,0,6),(2,1,5),(2,2,4),(2,3,3),(2,4,2),(2,5,1) :7 cases

...

(7,0,1), (7,1,1) :2 cases

(8,0,0) : 1 case

So number of orders =1+2+3+....+9=9*(1+9)/2=45

Answer 2

3^8=81*81=6561 possibilities.