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Probability and Permutations

Determine the probabilities of events when arrangement order matters

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Permutations and the Combination Lock

Combination Locks

Recall that a permutation is an arrangement in which order matters. For example, if you and two friends want to sit together during graduation and you want to know how many different orders you can arrange yourselves then you would look for a permutation.

In real life, these are used to calculate the total number of phones numbers, license plates, and serial numbers.

Credit: User:Mysid
Source: http://commons.wikimedia.org/wiki/File:Combination_lock.jpg
License: CC BY-NC 3.0

Ironically, all the different lock combinations on a number lock is an example of a permutation [Figure1]

Combination locks are a good example of a permutation because the order of the numbers is crucial to unlocking it. Let’s say your friend asks you to get his bike from school as a favor. When you get to the bike cages, however, you realize he never told you the actual combination to the lock.

Creative Applications

1. How many different unique combinations are there on a 4 number combination lock? How long is it going to take you to try all the combinations? (assuming it takes 5 seconds to enter one code)

2. What if your friend had a special lock that allows for both numbers and letter? How many different combinations do you need to try?

3. Based on the normal lock vs the special one, why do you think license plates include both numbers and letters?

4. How could you have an even greater amount of combinations in a 4 number lock?

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Image Attributions

  1. [1]^ Credit: User:Mysid; Source: http://commons.wikimedia.org/wiki/File:Combination_lock.jpg; License: CC BY-NC 3.0

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