Question

An ice cream shop has 8 types of ice cream and 20 types of toppings.

If one type of ice cream and two different types of toppings are chosen at random, how many combinations are possible?

A.

20 × 19 × 18






B.

20 × 20 × 20






C.

8 × 20 × 20






D.

8 × 20 × 19

Answer 1

So, the question is essentially, how many types of ice cream out of 8, multiplied to how many combinations of two different toppings from 20, right?

Answer 2

I Gess so Im not sure

Answer 3

You don't understand the problem?

Answer 4

No not really thats kinda why I came here

Answer 5

duly noted :)
Here's an example:
Suppose you have six shirts and 3 jackets, how many different ways can you pick a shirt and a jacket that go together?

Answer 6

The answer to that is something like this

six shirts and three jackets... so how many possible pairings?

Answer 7

18?

Answer 8

Well, you can pair the first shirt to any of the three jackets, so that makes three possibilities...

Answer 9

Oh, so you already got it :)
good.
So...
How many choices for your ice cream flavour?

Answer 10

I got 160 thats probaly rong tho

Answer 11

How did you get 18, by the way?

Answer 12

In my example... you just multiplied 6 and 3, right?

Answer 13

Yup

Answer 14

Well, same principle here :)
You have 8 ice cream types to choose from, right?
So
8, tentatively.
Now, how many toppings?

Answer 15

20

Answer 16

That's right, so for the ice cream type and the FIRST topping, you have
8 x 20 possibilities so far, right?

Answer 17

Yes

Answer 18

But then again, you need TWO toppings. How many choices for the SECOND topping?

Answer 19

Uh 20?

Answer 20

LOL
Are you sure?
Remember, that the two toppings are supposed to be DIFFERENT. That means you may no longer choose your first topping. So with that in mind, how many choices for the second topping?

Answer 21

I feel so dumb right now... 19?

Answer 22

Yep. :)
so... verdict
8 x 20 x 19

You may thank me later ^.^

Answer 23

Lol thank you ur a better teacher than my teacher :)

Answer 24

Heh... for all you know, I AM your teacher >:D
LOL Just kidding
Don't be so quick to judge though, I want to believe your teacher is trying his/her best ^.^
For now, I must leave....
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Terence out