a restaurant offers a choice of 6 appetizers, 14 entrees, 6 desserts, and 8 beve

Question

a restaurant offers a choice of 6 appetizers, 14 entrees, 6 desserts, and 8 beverages. Determine the number of possible meals if a diner intends to order two appetizers, an entree, a dessert, and a beverage, when a. the order of the appetizers is irrelevant, and they can be identical; b. the order of the appetizers is irrelevant, and they must be distinct; c. the order of the appetizers matters (fancy restaurant), but one can be repeated; and d. the order of the appetizers matters, and they must be distinct.

Explanation / Answer

6 appetizers, 14 entrees, 6 desserts, and 8 beverages. Determine the number of possible meals if a diner intends to order two appetizers, an entree, a dessert, and a beverage, when a. the order of the appetizers is irrelevant, and they can be identical; appetizer 6*6/2 answer=(18)14(6)8=12096 b. the order of the appetizers is irrelevant, and they must be distinct; appetizer=6*5/2= answer= 15(14)(6)8=10080 c. the order of the appetizers matters (fancy restaurant), but one can be repeated appetizer=6*6=36 answer=36*14(6)8=24192 ; and d. the order of the appetizers matters, and they must be distinct. appetizer=6*5=30 answer=36*14(6)8=20160

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