Invariance Principle

This short section states the Invariance Principle: the result of counting the objects in a set does not depend on the order in which the objects are counted, nor on the particular method used to count them — as long as the counting is done correctly, different valid orderings of the SAME counting process must arrive at the same final total.

Two examples, both drawn directly from the previous section, illustrate this. First, revisiting the Addition Principle example of choosing a shirt or a T-shirt: choosing first from the 4 shirts and then (as the alternative) from the 3 T-shirts gives the same total, $4+3=7$, as choosing first from the 3 T-shirts and then from the 4 shirts, $3+4=7$ — addition is commutative, so the order in which the two exclusive groups are considered makes no difference to the final count. Second, revisiting the Multiplication Principle example of ice-cream serving mode and flavour: choosing first from the 2 modes of serving and then from the 3 flavours gives the same total, $2\times3=6$, as choosing first from the 3 flavours and then from the 2 modes of serving, $3\times2=6$ — multiplication is likewise commutative. …