SOLUTION: A catering service offers 11 appetizers, 4 main courses, and 9 desserts. A banquet chairperson is to select 5 appetizers, 3 main courses, and 3 desserts for a banquet. In how many

Algebra ->  Permutations -> SOLUTION: A catering service offers 11 appetizers, 4 main courses, and 9 desserts. A banquet chairperson is to select 5 appetizers, 3 main courses, and 3 desserts for a banquet. In how many       Log On


   

Question 1098001: A catering service offers 11 appetizers, 4 main courses, and 9 desserts. A banquet chairperson is to select 5 appetizers, 3 main courses, and 3 desserts for a banquet. In how many ways can this be done?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
There are 11%2A10%2A9%2A8%2A7 ordered lists of 5 appetizers that can be written, but each set of 5 appetizers would be repeated in different order in 5%2A4%2A3%2A2 lists.
So, there are 11%2A10%2A9%2A8%2A7%2F%282%2A3%2A4%2A5%29 different sets of 5 appetizers that can be selected, from the 11 appetizers available.

There are 4%29 different sets of 3 main courses that can be selected from the 4 main courses available. (It is just a question of deciding which of the 4 main courses to exclude).

There are 9%2A8%2A7%2F%282%2A3%29 different sets of 3 desserts that can be selected from the 9 desserts available.

Combining the possible choices for appetizer, main course, and dessets selections, the number of posssible banquet menus is
.
Simplifying, you get