Question

Suppose you have a bag of Skittles with 27 blue Skittles, 18 green
Skittles, 32 red Skittles, and 10 yellow Skittles. You are very hungry and eat all Skittles
in this bag, but just one at a time.

a) How many possible orders are there to eat all Skittles in the bag?

b) If you pick Skittles from the bag in a random order to eat them, what is
the probability that you first eat all the red Skittles?

c) If you pick Skittles from the bag in a random order to eat them, what is
the probability that the red Skittles are the ones you eat last?

Answer 1

a)

number of all possible order =(87!/(27!*18!*32!*10!)=3.166*10⁴⁶

b)

number of ways all red Skittles in start =55!/(27!*18!*10!)) =5.019*10²²

therefore probability that you first eat all the red Skittles =5.019*10²² /3.166*10⁴⁶ =1.585*10^-24

c) probability that the red Skittles are the ones you eat last =32/87 (since there are 32 red Skittles out of total 87)