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 $\frac{5}{51}$.
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?
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