How many different varieties of pizza can be made if you have the following choice: small, medium, or large size; thin and crispy, hand-tossed or pan crust; and 12 toppings (cheese is automatic) from which you may select from 0 to 12?
a) 2 * 3c3
b) 2 * 4c3
c) 2 * 5c3
d) 2 * 6c3

There will be 36,864 different varieties.

Step-by-step explanation:

As given we have following options:

Size: small, medium, or large (3)

Style: thin and crispy, hand-tossed, or pan crust (3)

Toppings: 12 choices

Lets say the order of toppings does not matter.

So, number of ways of topping =

Hence, total number of different pizzas will be :

= 36864 different varieties.

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc