Question

You can choose from 25 flavours of ice cream and have enough money to get exactly 3 scoops.

How many different ice cream cones can you make if the order of the scoops are important,

but you are not allowed more than one of each flavour?

Answer 1

In the ice cream cone we can have 3 scoops only. No two scoops shall have the same flavour. Consider the scoops one by one.

For the first scoop we have 25 options to choose from.

After the first scoop is chosen, for the second scoop we are left with 24 options.

Similarly, when we choose the third scoop we can not the flavours chosen at first and second time. Hence we have 23 options for the 3rd scoop.

So, the number of ways we can choose 3 from 25 flavours is 25x24x23=13800 ways.

This is also known as Permutation. Given by ⁿP_r=n!/(n-r)!.

²⁵P₃= 25!/(25-3)! = 13800.