A pizza place offers ten different toppings. A special is a pizza with any three different toppings. How many different types of specials are offered?

Question

asked Jul 25, 2023 194k views

1 Answer

Mike Hildner · Answer 1 · 2023-07-30T09:14:27+0000

As given by the question

There are given that the total of 10 different topping

Now,

According to the question:

There is also talk about 3 different pizzas.

So,

The three different toppings from the 10 different toppings:

Then,

$\begin{gathered} 10C_3=(10!)/(3!(10-3)!) \\ 10C_3=(10!)/(3!(7)!) \\ 10C_3=(10*9*8*7!)/(3!(7)!) \\ 10C_3=(10*9*8)/(3*2*1) \end{gathered}$

Then,

$\begin{gathered} 10C_3=(10*9*8)/(3*2*1) \\ 10C_3=10*3*4 \\ 10C_3=120 \end{gathered}$

Hence, 120 different pizzas are possible.