Question

A local restaurant brags that they have “millions of options” for their ice cream sundaes. A customer can select one of 35 different ice cream flavors, any 3 out of 10 different candy toppings (assume you must pick 3), and can also decide whether to have or not have: whipped cream, chocolate syrup, caramel, and a cherry. They also serve the ice cream in one of 8 different dishes. Is their claim true or false? Support your answer with the relevant math.

Answer 1

Number of ways of selecting one flavor out of 35 is 35.

Number of ways of selecting 3 toppings out of 10 is

You can have Whipped cream or not. Likw wise you can have or not chocolate syrup, caramel, and a cherry. So number of ways of selecting these is 2*2*2*2 = 16

Number of ways of selecting one dish out of 8 is C(8,1) = 8.

So possible number of ways of different ice creams is

35 *120 * 16* 8 = 537600

That is company's claim true.