SOLUTION: A catering service offers 5 appetizers, 9 main courses, and 7 desserts. A customer is to select 4 appetizers, 2 main courses, and 4 desserts for a banquet. In how many ways can t

Algebra ->  Permutations -> SOLUTION: A catering service offers 5 appetizers, 9 main courses, and 7 desserts. A customer is to select 4 appetizers, 2 main courses, and 4 desserts for a banquet. In how many ways can t      Log On


   

Question 1150311: A catering service offers 5 appetizers, 9 main courses, and 7 desserts. A customer is to select 4 appetizers, 2 main courses, and 4 desserts for a banquet. In how many ways can this be done?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Use the nCr combination formula

or use a calculator that has the nCr function built in.
A third approach is to use Pascal's Triangle.


There are...
  • 5 C 4 = 5 ways to pick four appetizers (from a pool of five appetizers total)
  • 9 C 2 = 36 ways to pick two main courses (from a pool of nine main courses total)
  • 7 C 4 = 35 ways to pick four desserts (from a pool of seven desserts total)

side note: the order does not matter

This means that there are are 5*36*35 = 6300 ways to select a full meal that consists of 4 appetizers, 2 main courses, and 4 desserts (from a pool of 5 appetizers, 9 main courses, and 7 desserts)