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?
First, we need to calculate the total number of ways to select 2 flowers out of the 18 flowers in the vase:
18 choose 2 = 18! / (2! * 16!) = 153
Next, we need to calculate the number of ways to select 2 carnations out of the 6 carnations:
6 choose 2 = 6! / (2! * 4!) = 15
Finally, we can calculate the probability of selecting 2 carnations by dividing the number of ways to select 2 carnations by the total number of ways to select 2 flowers:
15 / 153 = 0.098 (rounded to three decimal places)
Therefore, the probability of selecting two carnations from the vase is approximately 0.098.