A big flower vase has 5 begonias, 6 carnations, and 7 tulips. Two flower are randomly selected without replacement. what is the probability of selection two carnation? write in simplest form.
To find the probability of selecting two carnations, we first need to find the total number of ways to select 2 flowers out of the 18 total flowers in the vase.
Total 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
Therefore, the probability of selecting two carnations is:
Probability = Number of ways to select 2 carnations / Total ways to select 2 flowers
Probability = 15 / 153
Probability = 5 / 51
Therefore, the probability of selecting two carnations is 5/51.