There are 3 appetizers, 8 main dishes, and 5 desserts on a restaurant menu. (a)
ID: 3304653 • Letter: T
Question
There are 3 appetizers, 8 main dishes, and 5 desserts on a restaurant menu.
(a) In how many different ways one can choose a full dinner course in this restaurant?
(b) On Friday night the appetizer and main dish menus are mixed and has a total of 11 choices. One can pick one for the appetizer and a different one for the main dish. How many different full courses one can have?
(c) On a special event on Saturday night the chef prepared 4 new dishes and offered them on both the appetizer and main dish menus. How different combinations you can make if you want your main dish to be different from your appetizer?
Explanation / Answer
(A)
1 Appetizer can be selected in 3C1 ways
1 main dist can be selected in 8C1 ways
1 dessert can be selected in 5C1 ways
total number of ways to select full dinner course = 3*8*5 = 120 ways
(B)
1 Appetizer from 11 can be selected in 11C1 ways
1 main dish from remaining 10 can be selected in 10C1 ways
1 dessert from 5 can be selected in 5C1 ways
Total number of ways to select full course dinner = 11*10*5 = 550
(C)
There are two possible cases here
1. Appetizer is selected from 4 new dishes, this can be done 4C1 ways and main dish is selected from remaiing 3 new dishes and 8 main dishes, this can be done ine 11C1 ways. Dessert can be selected in 5C1 ways. Hence total possible combinations are 4*11*5 = 220
2. Appetizer is selected from old list, this can be done in 3C1 ways and main dish is selected from 4 new dishes and 8 main dishes, this can be done in 12C1 ways. Dessert can be selected in 5C1 ways. Hence total possible combinations are 3*12*5 = 180
Possible number of full course dinner are 220 + 180 = 400
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