Below is a menu from a restaurant - Junior Cycle Mathematics - Question 2 - 2015

To calculate the angle for each sector, we use the formula:

$ext{Angle} = \frac{360^ ext{o}}{ ext{Number of options}}$

1. Main Course:

   • Number of options = 5 (Pizza, Spaghetti, Steak, Lamb, Salmon)
   • Angle for each sector = $\frac{360}{5} = 72^ ext{o}$

2. Dessert:

   • Number of options = 3 (Cheesecake, Chocolate Cake, Ice-cream)
   • Angle for each sector = $\frac{360}{3} = 120^ ext{o}$

To determine which course to add in order to maximize the number of different 3-course dinners, we consider the effects of adding one option to each course:

1. Extra Starter:

   • New choices for Starter = 5 (4 original + 1 new)
   • Number of dinners = $5 imes 5 imes 3 = 75$

2. Extra Main Course:

   • New choices for Main Course = 6 (5 original + 1 new)
   • Number of dinners = $4 imes 6 imes 3 = 72$

3. Extra Dessert:

   • New choices for Dessert = 4 (3 original + 1 new)
   • Number of dinners = $4 imes 5 imes 4 = 80$

Thus, the best option is to add an extra Dessert, which results in 80 different 3-course dinners being possible.