Probability

Question

Assume Gwen and Harry have 4 types of cones and 13 flavors of ice cream.

(1) In how many different ways can your order one cone and two scoops of ice cream?

Answer 1

They can choose a cone in 4 ways. For each cone, they have 13 choices of ice cream for the first scoop, then 13 choices for the second scoop. This gives us 4x13x13 ways, which is 676. Now this is the number only if we consider the order of the scoops to be important (for example if we consider vanilla on top of chocolate to be different from chocolate on top of vanilla).

 

If the order is not important, it is  4x(13x12/2 + 13) = 364, which is also

4x(1+2+3+4+...+12+13)