Question

when making an ice cream sundae, you have a choice of 4 types of ice cream flavors: chocolate (c), vanilla (v), moos tracks (m) or dark chocolate (d); a choice of 3 types of sauces: hot fudge (h), butterscotch (b) or strawberry (s); and a choice of 2 types of toppings: whipped cream (w) or fruit (f). if you are choosing only one of each, list the sample space in regard to the sundaes (combinations of ice cream flavors, sauces, and toppings) you could pick from.

Answer 1

There are 4 ice cream flavors :

chocolate (c), vanilla (v), moos tracks (m), and dark chocolate (d).

There are 3 types of sauces :

hot fudge (h), butterscotch (b), and strawberry (s).

There are 2 types of toppings :

whipped cream (w) and fruit (f)

The sample space are the combinations of ice cream flavors, sauces and toppings with one of each kind.

Listing down the sample spaces as {flavors, sauces, toppings}, will give us :

{c,h,w}, {c,h,f}, {c,b,w}, {c,b,f}, {c,s,w}, {c,s,f}

{v,h,w}, {v,h,f}, {v,b,w}, {v,b,f}, {v,s,w}, {v,s,f}

{m,h,w}, {m,h,f}, {m,b,w}, {m,b,f}, {m,s,w}, {m,s,f}

{d,h,w}, {d,h,f}, {d,b,w}, {d,b,f}, {d,s,w}, {d,s,f}

All in all, there are 24 sample spaces, which is also the product of 4 flavors, 3 sauces and 2 toppins (4 x 3 x 2 = 24)