There are a total of 5 + 6 + 4 = 15 flowers.
The probability of selecting a carnation on the first draw is 6/15.
Once a carnation has been selected, there are only 5 + 4 = 9 flowers left, of which 5 are begonias and 4 are tulips.
So the probability of selecting a second carnation after the first one has been removed is 5/9.
Therefore, the probability of selecting two carnations in a row without replacement is:
(6/15) x (5/9) = 1/3 x 5/9 = 5/27 or approximately 0.185.