Hi,

choice of eight toppings that can be added to a hamburger.

How many different hamburgers can be ordered?

Options of adding none up to 8 toppings(order not immportant) results in:

 8C0 + 8C1 + 8C2 + 8C3 + 8C4 + 8C5 + 8C6 + 8C7 + 8C8

 1 + 8 + 28 + 56 + 70 + 56 + 28 + 8 + 1

If one was to consider  the order of the toppings appropriate: 

Permutations would be used rather than combinations

 8P0 + 8P1 + 8P2 + 8P3 + 8P4 + 8P5 + 8P6 + 8P7 + 8P8

 

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