To find the probability distribution for the number of white roses chosen, we calculate the probabilities for choosing 0, 1, or 2 white roses.

There are a total of 10 roses (5 yellow, 3 red, 2 white).

Probability of choosing 0 white roses:

The probability of choosing 3 non-white roses is:

\(P(0) = \frac{8}{10} \times \frac{7}{9} \times \frac{6}{8} = \frac{42}{90}\)

Probability of choosing 1 white rose:

The probability of choosing 1 white and 2 non-white roses is:

\(P(1) = \left( \frac{2}{10} \times \frac{8}{9} \times \frac{7}{8} \right) \times 3 = \frac{42}{90}\)

The factor of 3 accounts for the different orders in which the roses can be chosen.

Probability of choosing 2 white roses:

The probability of choosing 2 white and 1 non-white rose is:

\(P(2) = \left( \frac{2}{10} \times \frac{1}{9} \times \frac{8}{8} \right) \times 3 = \frac{6}{90}\)

The factor of 3 accounts for the different orders in which the roses can be chosen.

Thus, the probability distribution table is: