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Which, in its final state gives:
This does look rather complicated, but remember that it follows from some fairly simple things
that we have built up on. Also notice that both the top fraction and the bottom fraction have .
Ah, yes! So that‟s why the order-not-eliminated and order-eliminated answers are the same:
⏟
⏟
While this works out beautifully in this example, it is not always true, and so we must take care
to observe whether order difference is important. We will see examples later where this
difference will come into play, but those situation are a bit more advanced.
Let‟s simplify this horrid notation a bit. Suppose that there are a total of
are to be drawn.
items and of those
Permutation – Order Does Matter
If order is not to be eliminated (in cases where order is important), then the number of ways to
select things from the given is called a permutation and is denoted:
( )
NOTE: ( ) , that is, factorial is not distributable!! Subtract first, then use
factorial.
For our numerator, we had selected 2 uncontaminated bushels from a total of 18 uncontaminated
bushels. According to our new notation, this can be written as:
( )
And this is precisely what we have written for the numerator!
For our denominator, we had selected 2 (general) bushels from a total of 20 (general) bushels,
since we want to know the total number of ways 2 objects can come out of 20.
Statistics for Decision-Making in Business © Milos Podmanik Page 123