Question

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?

Answer 1

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

${{18}\choose{2}} = \frac{18!}{2!(18-2)!} = 153$

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

${{6}\choose{2}} = \frac{6!}{2!(6-2)!} = 15$

Therefore, the probability of selecting 2 carnations is:

$P(\text{selecting 2 carnations}) = \frac{15}{153} = \frac{5}{51}$

So, the probability of selecting two carnations is $\frac{5}{51}$.