## A pizza parlor has a special on a three-topping pizza. How many different special pizzas can be ordered if the parlor has 8 toppings to choo

Question

A pizza parlor has a special on a three-topping pizza. How many different special pizzas can be ordered if the parlor has 8 toppings to choose from?

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1 week 2021-09-15T23:55:35+00:00 2 Answers 0

We assume the three toppings must be different.

Explanation:

Cheese :

3

choices

Toppings :

8

choices for the first,

7

for the second and

6

for the third, a total of

8

×

7

×

6

=

336

, IF the order of toppings were important — which it isn’t. This number is called the number of permutations .

Three things can be ordered in 6 ways (try this), so in the 336 permutations, there are groups of 6 that amount to the same combination :

123=132=213=231=312=321, etc.

So we have to divide the number of permutations by the number of orders to reach the number of combinations:

There are thus 336 : 6 = 56 possibilities for the toppings.

Since we need cheese AND toppings we multiply:

Number of different pizzas: 3 x 56 = 168.

Calculator : if you have the nCr function the answer would be:

3 x 8 nCr 3 = 168

Step-by-step explanation:

2. I think the answer is 24