Generalized Permuations and Combinations
Repetitions, Indistinguishable Objects, and Objects in Boxes
Permutations with Repetition
E X A M P L E S
Application of Theorem | Sampling with Replacement
| Example: Application of Theorem |
If I have the entire 17-disc CD collection of "21st Century Polka Music: Lawrence Welk Forever" but I can only take 6 CDs in my car, how many different ways can I choose the CDs to take with me?
Solution:
In this problem we determine that n = 17 (the number of things we're choosing from) and that r = 6 (the number of spots we have to put those items. Now using the formula of permutations = nr, we determine that
# of ways to take 6 CDs = 176
= 24,137,569
|
| 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) . |
|