A catering service offers

6

appetizers,

7

main courses, and

10

desserts. A customer is to select

5

appetizers,

4

main courses, and

5

desserts for a banquet. In how many ways can this be done?

There are 52920 ways to do the banquet

Step-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