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

There are a total of 4 types of Skittles (Red , Green , Blue , Yellow) in the bag

Answer a :

Total possible orders of eating the skittles = 4 x 3 x 2 x 1 = 24

(Since , in the first time , there are 4 varieties available

in the second time , there are 3 varities , the third time there are 2 and 1 in the last time )

Answer b:

Probability of eating all the red skittles in the first time = 1/4 = 0.25

Answer c:

Probability of eating the red skittles in the last time = (3/4) x (2/3) x (1/2) x 1 = 1/4 = 0.25

(Since , in the first time there are 3 varieties to pick other than red , for the second time 2 varieties to pick other than red , for the third time there is 1 variety to pick other than red and the last on Red , and each time you pick a variety a variety gets deducted from the bag )