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# i don't know how to do this

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706
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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?

May 6, 2019

#1
+2856
+1
May 6, 2019
#2
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Guest May 6, 2019
#3
+2856
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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

May 6, 2019
edited by CalculatorUser  May 6, 2019
edited by CalculatorUser  May 6, 2019
#4
+26856
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Hmmmmm.....   wouldn't it be 14 toppings?

14 c 2 = 91

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

May 6, 2019
#5
+6196
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14 is correct

Rom  May 6, 2019