(a) (i) To find the number of different three-course meals, multiply the number of choices for each course. There are 3 choices for the starter, 5 choices for the main course, and 3 choices for the dessert. Thus, the total number of three-course meals is:

\(3 \times 5 \times 3 = 45\)

(a) (ii) If customers choose only two of the three courses, consider the combinations:

• Starter and Main: \(3 \times 5 = 15\)
• Starter and Dessert: \(3 \times 3 = 9\)
• Main and Dessert: \(5 \times 3 = 15\)

Summing these gives:

\(15 + 9 + 15 = 39\)

(b) To divide 14 people into groups of 5, 5, and 4, use combinations:

\(\binom{14}{5} \times \binom{9}{5} \times \binom{4}{4} = 252252\)