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Followup:

Suppose we have 2^9 ways of choosing topics on a pizza. Then, if we want different topics on 3 pizzas, we can do that in 2^9C3 = (2^9*(2^9)-1*(2^9)-2)/3!

and if we want the same toppings on all the 3 pizzas, we already know that we can do that in 2^9 ways.

But what about the third option:

we want 2 same and one different topping for the 3 pizzas.

What formula will we use?

The answer is supposed to be 2^9*(2^9)-1

Suppose we have 2^9 ways of choosing topics on a pizza. Then, if we want different topics on 3 pizzas, we can do that in 2^9C3 = (2^9*(2^9)-1*(2^9)-2)/3!

and if we want the same toppings on all the 3 pizzas, we already know that we can do that in 2^9 ways.

But what about the third option:

we want 2 same and one different topping for the 3 pizzas.

What formula will we use?

The answer is supposed to be 2^9*(2^9)-1

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