Permutations with Repetition
Examples
| Example: Application of Theorem |
I recently inherited an unlimited supply of the
entire 17-disc CD collection of
"21st Century Polka Music: Lawrence Welk Forever".
If I can only take 6 CDs in my car, how many different ways can
I choose which CDs to take with me?
Solution:
Clearly
n = 17 (the number of things we're choosing from) and that r = 6
(the number of spots we have to put those items).
Since I have an unlimited supply of each disc, I can take multiple copies
of the same disc if I want, so we have permutations with repetition,
and the solution is
# of ways to take 6 CDs = 176
= 24,137,569
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| Example: Sampling with Replacement |
What is the probability of choosing 4 purple Nerf darts in a row from a jar containing 7 purple Nerf darts and 5 yellow Nerf balls, if an item is put back in the jar after each time it is drawn?
Solution:
There are 7 * 7 * 7 * 7 ways to choose a dart from the jar each time. Also, there are a total of 12 * 12 * 12 * 12 ways to choose four items from the jar.
Using the probability formula of (Successes) / (Total Outcomes) ,
we find that the solution is: (74) / (124) . |
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