Question

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

[AI-generated answer — Bot GPT 3.5]

First, we need to find the total number of ways to select 2 flowers out of the 18 flowers in the vase.

Total number of ways to select 2 flowers = 18 choose 2 = 18! / (2!(18-2)!) = 153

Next, we need to find the number of ways to select 2 carnations out of the 6 carnations in the vase.

Number of ways to select 2 carnations = 6 choose 2 = 6! / (2!(6-2)!) = 15

So, the probability of selecting two carnations = Number of ways to select 2 carnations / Total number of ways to select 2 flowers
= 15 / 153
= 5 / 51

Therefore, the probability of selecting two carnations is 5/51.