Question

At a local restaurant a new dinner menu is available that offers 4 courses 1 appetizer 1 salad 1 main dish and 1 dessert all for one price. There are 6 appetizers 2 salads 3 main dishes and 4 desserts. How many dinner outcomes are there possible

Answer 1

Number of Dinner Menu in the Restaurant = 4 =[1 appetizer+ 1 salad+ 1 main dish + 1 dessert]

Number of Different Appetizer = 6

Number of Different Salad =2

Number of Different Main Dishes = 3

Number of Different Desserts =4

Number of Different Dinner Outcomes

=[Choosing 1 appetizer among 6 appetizer] × [Choosing 1 Salad item among 2 salad Items] ×[Choosing 1 main Dish among 3 main Dishes] × [Choosing 1 dessert among 4 desserts]

=Order is not Important,so we will use the concept of combinatorics

`=_(1)^(6)\textrm{C}*_(1)^(2)\textrm{C}* _(1)^(3)\textrm{C} * _(1)^(4)\textrm{C}\\\\=6 * 2 * 3 * 4\\\\=144`

So, Number of Possible Dinner Outcomes = 144