How many different 3 topping pizzas can you make using cheese pepperoni sausage mushrooms anchovies green peppers or olives without doubling any toppings?
You have six different toppings. You want to make a three
topping pizza. You don't want to double any topping. This can be
expressed as the number of combinations of 6 things taken 3 at a
time. The answer is 20. The general case of the number of
combinations of N things taken P at a time is N! / (P! * (N - P)!).
N = 6. P is 3. Substituting, we get 720 / (6 * (6)), or 720 / 36,
or 20.