You have an unlimited supply of five different coloured pop-sticks, and want to make as many different coloured equilateral triangles as possible, using three sticks. One example is shown here. Two triangles are not considered different if they are rotations or reflections of each other.
How many different triangles are possible?
You can use 3 sticks of the same colour: 5 triangles
You can use 2 sticks of one colour, then one stick of another color: $5\times4=20$
You can also use 3 different colours of sticks. $5\times4\times3÷3=20$
Thus there are 45 possibilities.