Answer:
There are 52920 ways to do the banquet
Explanation:
* Lets revise the combination to solve this problem
- A combination is a collection of the objects where the order
doesn't matter
- The order is not important in this problem, so we can use the
combination nCr to find how many ways can this done
* Lets solve the problem
- A catering service offers 6 appetizers, 7 main courses, 10 desserts.
- A customer is to select 5 appetizers, 4 main courses, 5 desserts
for a banquet
∵ We want to select 5 appetizers from 6
∴ There are 6C5 ways to chose the appetizers
∵ 6C5 = 6
∴ There are 6 ways to chose the appetizers
∵ We want to select 4 main courses from 7
∴ There are 7C4 ways to chose the main courses
∵ 7C4 = 35
∴ There are 35 ways to chose the main courses
∵ We want to select 5 desserts from 10
∴ There are 10C5 ways to chose the desserts
∵ 10C5 = 252
∴ There are 252 ways to chose the desserts
- To find the number of ways to do the banquet multiply all the
answers above
∵ The total ways = 6C5 × 7C4 × 10C5
∴ The total ways = 6 × 35 × 252 = 52920
* There are 52920 ways to do the banquet