A restaurant offers a special pizza with 4 toppings. If the restaurant has 12 topping from which to choose, how many different special pizzas are possible?

To find the number of different special pizzas that can be made, we need to find the number of combinations of choosing 4 toppings out of 12 available toppings.

We can use the combination formula to solve this problem. The combination formula is given by:

C(n, r) = \frac{{n!}}{{r!(n-r)!}}

Where:
- n is the total number of items
- r is the number of items that we are choosing

In this case, we have 12 toppings to choose from and we want to choose 4 toppings. So we can plug in these values into the combination formula:

C(12, 4) = \frac{{12!}}{{4!(12-4)!}}

Now, let's simplify the expression:

C(12, 4) = \frac{{12!}}{{4!8!}}

Now, let's calculate the factorials:

C(12, 4) = \frac{{12 \times 11 \times 10 \times 9 \times 8!}}{{4! \times 8!}}

We can cancel out the 8! terms:

C(12, 4) = \frac{{12 \times 11 \times 10 \times 9}}{{4!}}

Simplifying further:

C(12, 4) = \frac{{12 \times 11 \times 10 \times 9}}{{4 \times 3 \times 2 \times 1}}

C(12, 4) = 12 \times 11 \times 10 \times 9 \times \frac{{1}}{{4 \times 3 \times 2 \times 1}}

C(12, 4) = 12 \times 11 \times 10 \times 9 \times \frac{{1}}{{24}}

Now let's calculate the product:

C(12,4)=12\times11\times10\times9\times\frac{{1}}{{24}}=495

Therefore, there are 495 different special pizzas that can be made from the 12 available toppings.

Answer: 495