The local ice cream shop sells ten different flavors of ice

The local ice cream shop sells ten different flavors of ice cream. How many different two-scoop cones are there? (A cone with a vanilla scoop on top of a chocolate scoop is considered the same as a chocolate cone with a scoop on top of a vanilla scoop.)

Solution

Total number of flavors = 10

Number of two-different scoops = 10C2 = 10!/(2!8!) = 10 * 9/2 = 45 varities

Since the chocolate on top and vanila on bottom is same as that chocolate on bottom and vanila on top

Hence we don\'t need to multiply the answer with 2, hence the number of options is equal to 45