A big flower vase has 5 begonias, 6 carnations, and 7 tulips. Two flower are randomly selected without replacement. what is the probability of selection two carnation? Express the answer in the simplest form of a fraction.
The total number of flowers in the vase is 5 + 6 + 7 = 18.
The probability of selecting a carnation on the first pick is 6/18.
After picking a carnation, there are only 5 carnations left and 17 total flowers left.
So, the probability of selecting a carnation on the second pick is 5/17.
Therefore, the probability of selecting two carnations is (6/18) * (5/17) = 30/306 = 5/51.
So, the probability of selecting two carnations is 5/51.