Question

Suppose you go to an ice cream shop which allows you to choose from 7 flavors of ice cream and 5 toppings. if you decide to get a sundae with 2 different types of ice cream and 3 different toppings, how many ways are there to make this choice?

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.

So, the answer is
`C(7,2)\cdot C(5,3)=(7!)/(2!5!)\cdot(5!)/(3!2!)=(6\cdot7)/(2)\cdot(4\cdot5)/(2)=210` ways.