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(male narrator) So now we're gonna talk about counting for a while.
And you're probably thinking, counting--I know how to count.
But we're gonna talk
about counting really large amounts of stuff.
So here's an example.
Suppose a restaurant...
you can have three choices of appetizer,
five choices for a main course,
um...and you're allowed to choose
exactly one from each category.
Um...how many different meal options do you have?
Well, there's several ways to approach this.
One way that I like is, uh...called a "decision tree."
So you start out here and say,
okay, I have how many choices for my appetizer?
I have three choices.
Uh...so I have 1, 2, 3 different directions I could go.
I could go soup direction, salad direction,
uh...and then breadsticks direction.
Then, uh...at each of those points,
I now have to decide on a main course,
and for each of those,
I now have 1, 2, 3, 4, 5 choices...
emanating out.
And so how many total choices do I have now?
You'll notice that there are five choices here,
another five here, another five there.
We end up with a total of 15 choices.
Uh...and that is how many meal options we have.
Now you may have noticed that where does that 15 come from?
Well, it's three choices for our first decision
times the five choices for the second decision,
'cause we have three of these little branchy tree things.
Uh...so we end up multiplying, uh...those choices together.
And that's exactly how this works.
Uh...so let's look at another one.
Suppose there's 21 novels and 18 volumes of poetry
that you...on a reading list for an English course.
How many different ways
can you select one novel and one volume of poetry?
Well, there's 21 choices for the novel,
18 choices for the poetry.
Uh...we multiply those together,
and that gives us a total of 378, uh...possibilities.
Uh...let's look at another one.
Now suppose that we're at a restaurant,
and we have three choices for the appetizer.
We have five choices for a main course,
and now two choices for dessert.
If we're allowed to choose
exactly one of them... uh...one of each of them,
then we would have 3 times 5, times 2, equals 30 choices.
Now it is important to note here that this is assuming
that we actually pick one from each of them.
That we're not gonna, you know, not pick one of them.
Okay, one more.
So suppose a quiz consists
of three true or false questions.
How many ways can a student answer this?
Well...so we have three questions.
Each of those questions has two choices.
Right?
Uh...so the first question... right, so three questions.
The first question, there are two choices.
For the second question, there are two choices.
For the third question, there are two choices.
And so altogether, there are two to the third--
or eight different ways, uh...that a student could answer
a three-question true or false quest...uh...quiz.