A big flower vase has 5 begonias, 6 carnations, and 7 tulips. Two folowers are randomly selected without replacement. What is the probability of selecting two carnations? Express the answer in simplest form of fraction.

Answer 1

There are 18 flowers in total, so the probability of selecting a carnation on the first draw is 6/18. Since we did not replace the selected flower, there are now only 17 flowers left, including only 5 carnations. Therefore, the probability of selecting a second carnation on the second draw is 5/17. To find the probability of both events happening (i.e. selecting two carnations in a row), we multiply the probabilities:

(6/18) * (5/17) = 30/306 = 5/51.

So the probability of selecting two carnations is 5/51.