Suppose that a restaurant offers a choice of 6 appetizers 10

Suppose that a restaurant offers a choice of 6 appetizers, 10 entrees, 6 desserts, and 8 beverages. Determine the number of possible meals if a diner intends to order two appetizers, an entr

Solution

Nos of appetizers = 6
Nos of ways two apetizers can be selected -
All different = ⁶C₂ = 15
All same = 6
All same as well as different = 15+6 = 21

Nos of entrees = 10
Nos of ways one entree can be selected = 10

Nos of desserts = 6
Nos of ways one dessert can be selected = 6

Nos of beverages = 8
Nos of ways one beverage can be selected = 8

So,
Number of ways in which all selected items with same and different apetizers are taken = 21 x 10 x 6 x 8 = 10080 ways
Number of ways in which all selected items with different apetizers are taken = 15 x 10 x 6 x 8 = 7200 ways
Number of ways in which all selected items with same apetizers are taken = 6 x 10 x 6 x 8 = 2880 ways