Question

A catering service offers 8 appetizers, 9 main courses, and 11 desserts. A customer is to select 4 appetizers, 7 main courses, and 10 desserts for a banquet. In how many ways can this be done?

Answer 1

The order doesn't matter.

$k$ objects can be chosen out of $n$ objects, when the order doesn't matter, in $C(n,k)=\dfrac{n!}{k!(n-k)!}$ ways.

$C(8,4)\cdot C(9,7)\cdot C(11,10)=\dfrac{8!}{4!4!}\cdot\dfrac{9!}{7!2!}\cdot \dfrac{11!}{10!}=\dfrac{5\cdot6\cdot7\cdot8}{2\cdot3\cdot4}\cdot\dfrac{8\cdot9}{2}\cdot11=\\=27,720$

There are 27,700 ways.