Combination of different main and side dishes

Question

John is going to a community cookout. At the cookout he can have a meal using any combination of 9 sides and 4 main dishes, as shown in the menu below. A.) John wants a meal with 3 different sides with his grilled veggies (main dish). How many different combinations for his meal are possible? B.) John's friend Tim wants a meal with 2 different sides with any type of main dish. How many different combinations are possible?

Answer 1

₉C₃ = 9! / ((9-3)!*3!) = 9*8*7 / 6 = 84

 

4*₉C₂ = 4 * 9! / ((9-2)!*2!) = 4 * 9*8/2 = 4 * 36 = 144