A pizza can be made with any of the following toppings: cheese, pepperoni, sausage, mushrooms, anchovies, green peppers, or olives. How many different three-topping pizzas can be made? Doubling of any topping is not allowed.

have the same problem did you figure it out ?

Well, let's do some delicious math to figure that out! Since we are making three-topping pizzas, we need to choose three toppings from the options provided.

So, we can use the combination formula to find the number of different three-topping pizzas. The formula is:

nCr = n! / (r!(n-r)!)

In this case, we have 7 toppings to choose from, and we want to choose 3 toppings.

7C3 = 7! / (3!(7-3)!)
= 7! / (3! * 4!)

And if we simplify that expression, we'll find:

7C3 = (7 * 6 * 5 * 4!) / (3! * 4!)
= (7 * 6 * 5) / (3 * 2 * 1)
= 35

So, there are 35 different three-topping pizzas that can be made. That's a lot of cheesy, topping-filled goodness! Enjoy your pizza party!

To determine the number of different three-topping pizzas that can be made without doubling any topping, we can use the concept of combinations.

We have 7 different toppings: cheese, pepperoni, sausage, mushrooms, anchovies, green peppers, and olives.

To choose 3 toppings without repetition, we can use the formula for combinations:

C(n, r) = (n!)/(r!(n-r)!),

where n is the total number of options, and r is the number of choices.

In this case, n = 7 (the number of toppings available), and r = 3 (the number of toppings we want to choose).

Using the formula, we get:

C(7, 3) = (7!)/(3!(7-3)!) = (7!)/(3!4!) = (7 x 6 x 5)/(3 x 2 x 1) = 35.

Therefore, there are 35 different three-topping pizzas that can be made without doubling any topping.

To calculate the number of different three-topping pizzas that can be made, we can use a combination formula.

The formula for combinations is given by:
C(n, r) = n! / (r!(n - r)!)

Where:
- n is the total number of items (toppings in this case),
- r is the number of items to choose (in this case, 3),
- ! denotes the factorial of a number (e.g., 4! = 4 x 3 x 2 x 1).

In this case, we need to calculate C(7, 3) since we have 7 different toppings to choose from.

Using the combination formula:
C(7, 3) = 7! / (3!(7 - 3)!)

Calculating the factorials:
C(7, 3) = (7 x 6 x 5 x 4 x 3 x 2 x 1) / ((3 x 2 x 1) x (4 x 3 x 2 x 1))

Simplifying the expression:
C(7, 3) = 35

Therefore, there are 35 different three-topping pizzas that can be made using the given toppings.

You'll need to use a factorial for this. You have 7 options, and are choosing 3 without replacement. Therefore, use a nCr combination. n = 7 toppings, r = 3 chosen.

The equation looks like this: (n!)/(r!*(n-r)!) = (7!)/(3!(7-3)!)
Calculate this out and you find 35 different 3-topping pizzas can be made.