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 camations? Express the answer in the simplest form of fraction.
• 17/30
• 65/150
• 13/17
• 13/30
To calculate the probability of selecting two carnations, we first need to find the total number of ways to choose 2 flowers from the total of 5 begonias, 6 carnations, and 7 tulips.
Total number of flowers = 5 (begonias) + 6 (carnations) + 7 (tulips) = 18 flowers
Total number of ways to choose 2 flowers from 18 = 18 choose 2 = 18! / (2!(18-2)!) = 153 ways
Next, we need to calculate the number of ways to choose 2 carnations from the total of 6 carnations.
Number of ways to choose 2 carnations out of 6 = 6 choose 2 = 6! / (2!(6-2)!) = 15 ways
Therefore, the probability of selecting two carnations = number of ways to choose 2 carnations / total number of ways to choose 2 flowers = 15 / 153 = 5 / 51
So the answer is not in the list provided, but the correct answer in simplest form is 5/51.