In a bag of marbles, there are 5 brown, 6 yellow, 4 blue, 3 green, and 2 orange. What is the probability of getting 1 brown and 2 orange marbles if 3 are taken at a time?
First, there are 5 + 6 + 4 +3 + 2 = 20 marbles total in the bag.
the probability of getting a brown, an orange, and another orange is equivalent to:
the probability of a brown * the probability of 2 oranges.
The probability of a brown marble is just (5 choose 1), or 5 ways to choose it.
Next, the number of ways to get 2 orange marbles is just (2c2), or 1.
Finally, the total number of ways to choose three marbles(our divisor) is (20 choose 3), since you're picking 3 out of 20 total
This gives us:
(5c1) * (2c2) / (20c3) =
5 / 1140 =