At her favorite ice cream store, Saga can put up to two toppings on an ice cream cone. If there are 106 different ways she can choose toppings (including the choice of no toppings), how many different toppings are there?

Guest May 6, 2019

#1**+1 **

This question has been answered before --> https://web2.0calc.com/questions/ice-cream-store-two-topping-on-ice-cream-cone-106

CalculatorUser May 6, 2019

#3**+1 **

**Sorry!** Here I will solve it myself.

2 cases here

case 1 : **1 topping**

case 2 : **2 toppings**

In all there should be 106 - 1 (no toppings case) = **105** ways with 2 cases added together.

OK....

Notice how if you have x toppings with y ways there are y/x different toppings.

So we have 1 topping and 2 toppings with 105 ways. That means there are **35 different toppings**

This makes sense. Because :

CASE 1 : 1 * 35 = 35 ways

CASE 2 : 2* 35 = 70 ways

CASE 3 : Not toppings (1)

So add three cases together 35 + 70 + 1 = 106

So there you have it! :D :D :D

CalculatorUser May 6, 2019

#4**0 **

Hmmmmm..... wouldn't it be 14 toppings?

14 c 2 = 91

PLUS 14 single toppings = 105 PLUS NO TOPPING = 106.

ElectricPavlov May 6, 2019