An ice cream shop offers 31 flavors of ice cream, 5 different sundae sauces, and

Question

An ice cream shop offers 31 flavors of ice cream, 5 different sundae sauces, and 8 dry sundae toppings. How many two scoop sundaes could you create if two different ice cream flavors are used with one Sundae sauce and three different dry toppings? Ingredients don’t need to go an any particular order An ice cream shop offers 31 flavors of ice cream, 5 different sundae sauces, and 8 dry sundae toppings. How many two scoop sundaes could you create if two different ice cream flavors are used with one Sundae sauce and three different dry toppings? Ingredients don’t need to go an any particular order

Explanation / Answer

Number of ways in which 2 different flavors can be selected from 31 = 31C2

= 31! / (29! x 2!)

= 465

Number of ways in which sundae sauce can be selected = 5

Number of ways in which 3 sundae toppings can be selected from 8 = 8C3

= 8!/(3!x5!)

= 56

Number of two scoop sundaes that can be made = 465 x 5 x 56

= 130,200

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