A bag contains 5 red skittles, 4 yellow skittles, 3 green skittles, 2 orange skittles, and 2 purple skittles. If five skittles are removed, what is the probability that exactly two of them are green?
There are 16 red Skittles. 25% of the bag is orange. 1/8 of the Skittles are yellow. The rest of the Skittles are green.
To find the probability of exactly two green skittles being chosen, we need to calculate the total number of ways to select five skittles and then determine the number of favorable outcomes (two green skittles).
The total number of ways to select five skittles can be found using combinations, which is represented by "C(n, k)". In this case, we have a total of 16 skittles, so n = 16. We want to select 5 skittles, so k = 5.
So the total number of ways to select five skittles is:
C(16, 5) = 16! / (5! * (16-5)!) = 4368
Next, we need to determine the number of favorable outcomes, which is selecting exactly two green skittles. We have 3 green skittles, so we choose 2:
C(3,2) = 3! / (2! * (3-2)!) = 3
Finally, we calculate the probability by dividing the number of favorable outcomes by the total number of outcomes:
Probability = Number of Favorable Outcomes / Total Number of Outcomes
= 3 / 4368
= 1 / 1456
Therefore, the probability of exactly two green skittles being chosen is 1/1456.