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)=(n!)/(k!(n-k)!)` ways.

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

There are 27,700 ways.