Acatering 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

10

step-by-step explanation:

7+3=10