Question

An ice cream shop has a selection of 10 flavors of ice cream and 5 toppings. The first menu option lets you pick three flavors and two toppings for $3.75. How many combinations can be created with the first menu option, assuming you pick different flavors of ice cream and different toppings?

Answer 1

Answer:

Here we want to find all the possible combinations that we can make,

First, let's define the selections that we have, and the number of options for each one of these selections. (Remember that each option can be selected only once)

we have 3 flavors and 2 toppings, so let's analyze this case:

First flavor ----- here we have 10 options

Second flavor ---- because we already selected one before, now we have 9 options.

Third flavor ---- because we already selected two before, now we have 8 options.

First topping --- here we have 5 options,

Second topping --- because we already selected one before, here we have 4 options.

Now the total number of possible combinations will be equal to the product between the number of options for each selection:

C = 10*9*8*5*4 = 14,400