Question

How many different 3 topping pizzas can be made if 10 different toppings are available?

Answer 1

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Answer:

  120

Step-by-step explanation:

We assume the order of the toppings does not matter. Then the number of interest is the number of combinations of 10 toppings taken 3 at a time. That is given by ...

  10C3 = C(10, 3) = 10!/(3!(10 -3)!) = 10·9·8/(3·2·1) = 120

120 different 3-topping pizzas can be made if 10 toppings are available.

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Additional comment

If order matters, then 10 choices can be made for the first topping, 9 for the second, and 8 for the third, for a total of 10×9×8 = 720 different pizzas.

Answer 2

Assuming you can’t use the same topping twice,
10 x 9 x 8 = 720