Question 109952: The ice cream parlor can make a sundae using any combination of 6 toppings and 4 different types of ice cream, as shown on the menu below.
Types of Ice Cream Sundae Toppings
vanilla hot fudge
chocolate hot caramel
strawberry cookie crumbs
coffee nuts
candy pieces
chocolate sprinkles
A. Anne wants a sundae with 2 different toppings on chocolate ice cream. How many different combinations of toppings for Anne’s sundae are possible? Show your work and explain why you did each step.
B. Will wants a sundae with 3 different toppings on any type of ice cream. How many different sundae combinations are possible? Show your work and explain why you did each step
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The ice cream parlor can make a sundae using any combination of 6 toppings and 4 different types of ice cream, as shown on the menu below.
Types of Ice Cream Sundae Toppings
vanilla hot fudge
chocolate hot caramel
strawberry cookie crumbs
coffee nuts
candy pieces
chocolate sprinkles
A. Anne wants a sundae with 2 different toppings on chocolate ice cream. How many different combinations of toppings for Anne’s sundae are possible? Show your work and explain why you did each step.
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6C2 = 6*5/1*2 = 15
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There are 6 ways to choose the 1st topping and 5 ways to choose the 2nd
topping. There there are 30 arrangements of 2 toppings. But each pair
of toppings appears twice in the list of arrangements: for example,the
pair coffee nots/candy pieces appears appears twice but is only one pair.
So dividing all the arrangements by 2 gives 15 pairs (or combinations)
of two toppings.
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B. Will wants a sundae with 3 different toppings on any type of ice cream. How many different sundae combinations are possible? Show your work and explain why you did each step
6C3 = 6*5*4/1*2*3= 20
Same reasoning as above: 120 arrangements but 6 ways to arrange the three
elements of each group (combination).
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Cheers,
Stan H.
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