I was a little confused as I got a different response compared to the correct answer which was 189/1615.
If 6 science fair exhibits are chosen at random from 4 biology, 7 chemistry, and 9 physics exhibits to go to the county final, what is the probability that there will be two from each subject area?
To find the probability of selecting two exhibits from each subject area, we need to calculate two probabilities: the probability of selecting 2 biology exhibits, 2 chemistry exhibits, and 2 physics exhibits.
First, let's calculate the probability of selecting 2 biology exhibits out of 4. We can use combination formula.
The number of ways to choose 2 biology exhibits out of 4 is given by C(4, 2) = 4! / (2!(4 - 2)!) = 6.
The total number of ways to choose any 6 exhibits from the total pool (4 biology, 7 chemistry, and 9 physics) is given by C(20, 6) = 20! / (6!(20 - 6)!) = 38,760.
So, the probability of selecting 2 biology exhibits is 6/38,760.
Similarly, the probability of selecting 2 chemistry exhibits out of 7 is C(7, 2) = 7! / (2!(7 - 2)!) = 21/6 = 7/3,528.
The probability of selecting 2 physics exhibits out of 9 is C(9, 2) = 9! / (2!(9 - 2)!) = 36/72 = 1/2.
Now, to find the combined probability of selecting 2 exhibits from each subject area, we multiply these individual probabilities together.
Probability = (6/38,760) * (7/3,528) * (1/2) = 189/1615.
Therefore, the probability that there will be two exhibits from each subject area is 189/1615.