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?

Answer 1

First, we need to find the total number of ways to choose 2 flowers from the vase, which is given by the combination formula:

Total ways = (5+6+7) choose 2 = 18 choose 2 = 153 ways

Next, we need to find the number of ways to choose 2 carnations from the vase, since we want to find the probability of selecting two carnations. There are 6 carnations in the vase, so the number of ways to choose 2 carnations is given by the combination formula:

Number of ways to choose 2 carnations = 6 choose 2 = 15 ways

Therefore, the probability of selecting two carnations is:

Probability = (Number of ways to choose 2 carnations) / (Total ways)
Probability = 15 / 153
Probability = 0.098

Therefore, the probability of selecting two carnations from the vase is approximately 0.098 or 9.8%.