A big flower vase has 8 lilies, 9 roses, and 4 daisies. Two flowers are randomly selected without replacement. What is the probability of selecting two lilies? Express the answer in the simplest form of fraction.
First, let's find the total number of ways we can choose 2 flowers out of the 21 flowers in the vase:
${21 \choose 2} = \frac{21!}{2!(21-2)!} = \frac{21 \times 20}{2 \times 1} = 210$
Next, let's find the total number of ways we can choose 2 lilies out of the 8 lilies in the vase:
${8 \choose 2} = \frac{8!}{2!(8-2)!} = \frac{8 \times 7}{2 \times 1} = 28$
Therefore, the probability of selecting two lilies is:
$\frac{28}{210} = \frac{2 \times 2 \times 7}{2 \times 3 \times 5 \times 7} = \frac{4}{15}$
So, the probability of selecting two lilies is $\frac{4}{15}$.