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 fraction

Answer 1

The total number of flowers in the vase is 5 begonias + 6 carnations + 7 tulips = 18 flowers.

The probability of selecting a carnation on the first draw is 6/18.

Since we do not replace the first carnation that was drawn, there are now only 17 flowers left in the vase, with 5 begonias and 7 tulips remaining.

The probability of selecting a carnation on the second draw after selecting a carnation on the first draw 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.