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