MATH SOLVE

3 months ago

Q:
# A catering service offers 6appetizers, 7main courses, and 10desserts. A customer is to select 5appetizers, 4main courses, and 5desserts for a banquet. In how many ways can this be done?

Accepted Solution

A:

Answer:There are 52920 ways to do the banquetStep-by-step 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