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## how many 4-topping pizzas can be made if there were

**Ask: **how many 4-topping pizzas can be made if there were 10different toppings

**Answer:**

__210__ kinds of four-topping pizza can be made.

**Step-by-step explanation:**

10×9×8×7/4! = 5,040/4×3×2×1 = 5,040/24 = 210

## why everyone loves pizza?

**Ask: **why everyone loves pizza?

Well, pizza is junk food which are bad for you. When we eat junk food the first time it will make you want to eat more. It makes you addicted to it, food company like to do this because more people will buy their product.

well its simple , pizza is delicious:)

## why everyone loves pizza?

**Ask: **why everyone loves pizza?

because its every likes it because its a junk food what we eat every day y because we are habbitated by eating all those food items

Well, pizza is junk food which are bad for you. When we eat junk food the first time it will make you want to eat more. It makes you addicted to it, food company like to do this because more people will buy their product.

## pineapple on top of pizza

**Ask: **pineapple on top of pizza

Yummy sounds delicious makes me wanna order some

## What the solution for this problem At enzos pizza parlor,

**Ask: **What the solution for this problem At enzos pizza parlor, there are seven different toppings, where a costumer can order any number of these toppings. If you dine at the said pizza parlor wiht how many possible toppings can you order your ouzza

If there are 7 topping and also 7 choices is needed. we'll be having

=(7-7)!

=0!

=1

## there are eight different toppings available how many different pizzas

**Ask: **there are eight different toppings available how many different pizzas can be ordered with exactly three toppings?

As arrangement don't count, this is a combination problem

thus # of different pizzas that can be ordered = 8C3

= 8 .7 .6/3!

= 56 different pizzas

## is pizza with toppings heterogeneous??

**Ask: **is pizza with toppings heterogeneous??

**Answer:**

YES

**Explanation:**

The heterogeneous mixture has a non-uniform composition and has two or more phases. It can be separated out physically. The pizza is obviously physically separated from its toppings.

#CarryOnLearning

## what makes food delicious and unique?

**Ask: **what makes food delicious and unique?

**Answer:**

Flavor is the blend of taste, aroma, and feeling factor sensations. These three sensations occur when food stimulates receptors in our mouth and nose. Let's go back to the chemicals. It is because of the chemical nature of food that the senses are considered chemical sensors.

**Explanation:**

## a restaurant offers four sizes of pizza,two types of crust,and

**Ask: **a restaurant offers four sizes of pizza,two types of crust,and eight toppings.how many possible combinations of pizza with one topping are there?

So, 4 sizes ex. (S, M, L, XL) times two types of crust (A, B), there's 8 combinations ( sa sb ma mb la lb xla xlb) then 8 toppings and only one toppings 8×8=64. There's 64 combinations.

## At Enzo's pizza parlor , there are seven different topings

**Ask: **At Enzo's pizza parlor , there are seven different topings , where a costumer can order any number of these toppings.If you dine at the said pizza parlor,with how many possible toppings can you actually order your pizza?

**Answer:**

127

**Step-by-step explanation:**

The **sum rule of the fundamental principle of counting** states that if we have __X ways of doing something__ and __Y things of doing another thing__, and __we cannot do both at the same time__, then there are__ X+Y ways to choose one of the actions__.

In this problem, __the action that we are choosing is getting pizza__. __The different ways of getting pizza is the number of toppings.__ We can have a pizza with 2 toppings, 4 toppings, etc. We **add **all these ways to know how many ways can we order pizza.

Since we don't care about the order in which our toppings go to our pizza, we use **combination**. A combination is a selection of items from a pool of possible ones such that the order does not matter. It does not matter if a topping comes first or second. What matters is if it is in the pizza or not.

The formula for taking r things from n possible ones, with no particular order is given by the formula is expressed by the formula:

[tex]\frac{n!}{r!(n-r)!}[/tex]

Since there are 7 toppings to choose from, our n is 7.

For our pizza, we can use 1, 2, 3, 4, 5, 6, or 7 toppings. This is what I was referring earlier with how we can order pizza. Let us take each amount of toppings, and then add them all together.

- The pizza has 1 topping.

We let n be 7, and r be 1. Substituting gives us:

[tex]\frac{n!}{r!(n-r)!}\\\\\frac{7!}{1!(7-1)!}\\\\\frac{7!}{1!6!}\\\\\frac{7*6!}{6!}\\\\7[/tex]

__There are 7 ways to get a pizza with 1 topping.__

- The pizza has 2 toppings.

We let n be 7, and r be 2. Substituting gives us:

[tex]\frac{n!}{r!(n-r)!}\\\\\frac{7!}{2!(7-2)!}\\\\\frac{7!}{2!5!}\\\\\frac{7*6*5!}{2*5!}\\\\7*3\\\\21[/tex]

__There are 21 ways to get a pizza with 2 toppings.__

- The pizza has 3 toppings.

We let n be 7, and r be 3. Substituting gives us:

[tex]\frac{n!}{r!(n-r)!}\\\\\frac{7!}{3!(7-3)!}\\\\\frac{7!}{3!4!}\\\\\frac{7*6*5*4!}{3*2*4!}\\\\7*5\\\\35[/tex]

__There are 35 ways to get a pizza with 3 toppings.__

- The pizza has 4 toppings.

We let n be 7, and r be 4. Substituting gives us:

[tex]\frac{n!}{r!(n-r)!}\\\\\frac{7!}{4!(7-4)!}\\\\\frac{7!}{4!3!}\\\\\frac{7*6*5*4!}{4!*3*2}\\\\7*5\\\\35[/tex]

__There are 35 ways to get a pizza with 4 toppings.__

- The pizza has 5 toppings.

We let n be 7, and r be 5. Substituting gives us:

[tex]\frac{n!}{r!(n-r)!}\\\\\frac{7!}{5!(7-5)!}\\\\\frac{7!}{5!2!}\\\\\frac{7*6*5!}{5!*2}\\\\7*3\\\\21[/tex]

__There are 21 ways to get a pizza with 5 toppings.__

- The pizza has 6 toppings.

We let n be 7, and r be 6. Substituting gives us:

[tex]\frac{n!}{r!(n-r)!}\\\\\frac{7!}{6!(7-6)!}\\\\\frac{7!}{6!1!}\\\\\frac{7*6!}{6!}\\\\7[/tex]

__There are 7 ways to get a pizza with 6 toppings.__

The pizza has 7 toppings.

We let n be 7, and r be 7. Substituting gives us:

[tex]\frac{n!}{r!(n-r)!}\\\\\frac{7!}{7!(7-7)!}\\\\\frac{7!}{7!0!}\\\\\frac{7!}{7!}\\\\1[/tex]

__Note that 0! = 1__

__There is 1 way to get a pizza with all 7 toppings.__

__We add all these ways together to get how many ways we can make pizza.__

[tex]7+21+35+35+21+7+1 = 127[/tex]

__There are __**127 ways**__ to create a pizza.__

__Shortcut:__

If you notice, the answer to the number of ways of choosing 4 toppings from 7, and 3 toppings from 7 are both 35. There is a shortcut to finding the combination.

__If you take the combination of r things from n possible ones. It is the same as getting the combination of ____(n-r) things____ from ____n possible ones____. __

Since earlier, we were getting the ways to get 4 toppings, we can use this concept to say that it is the same as getting 3 toppings, since 7-4 = 3.

If you substitute it to the formula.

[tex]\frac{n!}{r!(n-r)!}\\[/tex]

compare it when r is (n-r)

[tex]\frac{n!}{r!(n-r)!}\\\\\frac{n!}{(n-r)!(n-[n-r])!}\\\\\frac{n!}{(n-r)!(n-[n-r])!}\\\\\frac{n!}{(n-r)!(n-n+r)!}\\\\\frac{n!}{(n-r)!(r)!}\\[/tex]

**It's the same thing**, since we just reversed the order of the denominator.

To know more about combination and similar problems, click here.

brainly.ph/question/494651

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brainly.ph/question/1994449

brainly.ph/question/103634

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