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(male narrator) So 50 students were surveyed
and asked if they were taking a social science, humanities,
or natural science course the next quarter,
and here are the survey results.
And we're wondering how many students
are only taking a social science class?
Uh...because these 21 who are taking a social science class
may have also been taking some others.
So, uh...to work with this,
let's bring in, again, a Venn diagram.
This is gonna help us, uh...picture what's going on.
Uh...and we have sort of our universal set here,
which we may or may not need to deal with,
but...I'll go ahead and draw it in.
So let's start
with the most specific piece of information here.
So we know that 3 students were taking all three courses,
so in our inter... middle intersection here
containing all three sets, we got 3 people.
We also got 7 outside of all three, uh...sets,
and so we'll go ahead and mark that in.
I'm gonna mark these off as I work with them.
So now 7 students were taking
a social science and a natural science class,
which means those 7 people would be in the intersection
of the SS and MS sets here.
Of those 7, 3 are taking all three,
which leaves 4 students who were taking, uh...
a social science and natural science
but not a humanities class.
Now 10 were taking a humanities and a natural science class,
of which 3 are taking all three,
so which leaves 7, uh...for this part of the set.
Uh...and then, there were 9
taking social science and humanities--
3 of which are taking all three,
which leaves 6 for that portion of the set.
Now...we can say, uh...we had 21 students
taking a social science class, we have 6 and 4 is 10 is...
plus, uh...plus 3 more is 13 students here.
So we got 13 students already accounted for,
so 21 minus those 13 students leaves us with 8 students,
uh...for this region here.
And that lets us answer our question.
There are 8 students taking only a social science class.