(i) To find the probability that the sum of the numbers on the three cards is 11, consider the possible combinations: (3, 4, 4), (4, 3, 4), or (4, 4, 3). The probability for each combination is calculated as follows:

\(\text{Prob} = \left( \frac{4}{10} \times \frac{6}{9} \times \frac{5}{8} \right) \times 3C1 = \frac{360}{720} = \frac{1}{2}\)

Alternatively, using combinations:

\(\frac{\binom{6}{2} \times \binom{4}{1}}{\binom{10}{3}} = \frac{1}{2}\)

(ii) The probability distribution table for the sum of the numbers on the three cards is:

Calculations for each sum:

• \(P(3, 3, 3) = \frac{4}{10} \times \frac{3}{9} \times \frac{2}{8} = \frac{24}{720}\)
• \(P(3, 3, 4) = \frac{4}{10} \times \frac{3}{9} \times \frac{6}{8} \times 3C1 = \frac{216}{720}\)
• \(P(4, 4, 4) = \frac{6}{10} \times \frac{5}{9} \times \frac{4}{8} = \frac{120}{720}\)