(i) To find the probability that Noor chooses exactly one T-shirt, we use combinations. The total number of ways to choose 3 items from 12 is given by \(\binom{12}{3}\).

The number of ways to choose 1 T-shirt from 3 is \(\binom{3}{1}\), and the number of ways to choose 2 items from the remaining 9 (blouses and jumpers) is \(\binom{9}{2}\).

Thus, the probability is:

\(\frac{\binom{3}{1} \times \binom{9}{2}}{\binom{12}{3}} = \frac{3 \times 36}{220} = \frac{108}{220} = \frac{27}{55}\)

(ii) The probability distribution table for X is constructed by considering the possible values of X (0, 1, 2, 3) and their respective probabilities: