A big flower vase has 5 begonias, 6 carnations, and 7 tulips. two flowers are randomly selected without replacement what is the probability of selecting two carnations? express the answer in the simplest form of a fraction
There are a total of 5 begonias, 6 carnations, and 7 tulips, so there are 6+5+7 = 18 flowers in total.
The probability of selecting a carnation on the first pick is 6/18 = 1/3.
After selecting a carnation, there are now 5 begonias, 5 carnations, and 7 tulips left, so there are 5+5+7 = 17 flowers left in total.
The probability of selecting another carnation on the second pick is now 5/17.
Therefore, the probability of selecting two carnations is (1/3) * (5/17) = 5/51.
So, the probability of selecting two carnations is 5/51.