Unformatted text preview: ssen (U of A) Counting 3/7 Counting n
Even better, there is a handy formula for computing (k ) which follows
from the multiplication principle we derived earlier. Theorem
For 1 k n (and the convention that 0! = 1), the following holds:
n
k Van Essen (U of A) = n!
.
k ! (n k ) ! Counting 4/7 Proof of the theorem
First, recall that the number of ways to arrange n objects is n !.
With k …xed, we can think about each such arrangement of the n
objects as being “built” be the following three step process:
1
2
3 Choose k of the objects to be the initial “block.”
Arran...
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 Spring '12
 Vanessen

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