word problem

Question

Hello,

 

I would greatly appreciate it. If you can help me with this word problem. 

 

How many different two toppings combination pizzas can be made by using T different toppings at Pete's Pizzeria? Explain how you know?

Answer 1

choose 2 items from T number of items

use the formula n!/r!(n-r)! where n=T and r=2

 

T!/2!(T-2)!

[T(T-1)(T-2)(T-3)...]/2![(T-2)(T-3)...]

simplify

T(T-1)/2

examples:

T=4 toppings

4(3)/2=12/2=6

A,B,C,D are the toppings

AB,AC,AD,BC,BD,CD

T=5 toppings

5(4)/2=20/2=10 toppings

A,B,C,D,E are the toppings

AB,AC,AD,AE,BC,BD,BE,CD,CE,DE