An ice cream parlor offers 37 different flavors of ice cream

An ice cream parlor offers 37 different flavors of ice cream. One of its items is a bowl consisting of three scoops of ice cream, each a different flavor. How many such bowls are possible? There are bowls of three-flavor ice cream possible.

Solution

3 flavours from 37 flavours can be selected in ³⁷C₃ ways

==> 37!/[(37 -3)! 3!]

==> 37!/[34! 3!]

==> (37*36*35)/(3*2*1)

==> 46620/6

==> 7770

Hence 7770 bowls of three flavour ice cream possible.