ShmoopTube

00:03

Here’s your shmoop du jour, brought to you by pineapple.

00:06

It belongs on a pizza like your mom belongs on one of your dates.

00:10

Ethan must choose two toppings for his pizza from this selection:

00:14

pepperoni, olives, mushrooms, sausage, and pineapple.

00:19

How many different combinations of two toppings are there?

00:22

And here are the potential answers...

00:25

So Ethan has to settle on a couple of toppings for his pie.

00:28

But, he’s super-thorough, so he wants to make sure he isn’t missing any of the combos.

00:33

Let’s say he wants pepperoni.

00:35

In that case, there would be 4 combinations…pep and olive, pep and shroom, pep and sausage,

00:41

and pep and pineapple.

00:43

Okay, what about if we do the same thing for olives?

00:45

Well… still 4 combos… except we already did pep and olive, so really just three more.

00:53

Same thing happens when we get to mushrooms…

00:55

…we’ve already covered two of the possible combos involving fungi,

00:59

so there are now just 2 combos remaining.

01:02

And by the time we get to sausage…the only thing it hasn’t yet been paired with is pineapple…

01:07

and we’re done.

01:08

So as each slot gets filled, we have one fewer option to choose from…

01:12

In other words, our number of possible combinations will be four plus three plus two plus one…

01:18

…or 10. Answer C.

01:20

Ethan can finally complete his order and.... he decides to get a calzone.

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