Counting Ii Statistics Worksheet Page 4
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There are n di↵erent ways to choose 1 object from a set that has n objects.
n
Thus,
= n.
1
Similarly, there are exactly n di↵erent options for choosing n
1 objects
from a set of n objects. To see this, notice that deciding which of the n
1
objects that you will take from a set of n objects is the same as deciding
which 1 object you will leave behind. So the number of ways you can take
n
1 objects is the same as the number of ways you can leave 1 object. That
n
n
n
is to say,
=
. Hence,
= n
n 1
1
n 1
Once we fill in this new information on Pascal’s triangle it looks like
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n
Before moving on, let’s look back at the last rule that we found:
=
n 1
n
. The argument we gave there generalizes, in that taking k objects from
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