Monday, April 9, 2007

My Take On Permutations

First off I would like to say that this is a interesting way to learn our new unit, but it will also be quite interesting to see what we all come up with and if well we know what were talking about after all. So here i go;;;;

A permutation is an arrangement of objects in different orders. The order of the arrangement is important!!
For example, the number of different ways 3 students can enter school can be shown as 3!, or 3·2·1, or 6. There are six different arrangements, or permutations, of the three students in which all three of them enter school.

The notation for a permutation: nPr
n is the total number of objects
r is the number of objects chosen (want)
(Note if n = r then nPr = n!)

Some examples of Permutations:
1. 5P5 = 5·4·3·2·1 = 120
2. 7P5 = 7·6·5·4·3 = 2520

Here are some Questions you may see and how you can figure out how to do them using the Permutations Formula (nPr) in use!!

1. What is the total number of possible 5-letter arrangements of the letters s,w,i,n,g if each letter is used only once in each arrangement?
5P5 = 5·4·3·2·1 = 120
( 5 letters to choose from, n#, want 5-letter arrangements, r#)

2. How many different 3-digit numerals can be made from the digits of 45678 if a digit can appear just once in a numeral?
5P3 = 5·4·3 = 60
( 5 numbers to choose from, n#, want 3-digit numerals, r#)

Also, as I was searching around I found some interesting websites on Perms & Cons that were helpful to me and thought I would share them with the rest of the class;

1. ( This website gives the break down of how you start out on a question and take the information and put it into the formula)

2. (If your not to sure your doing this unit to right you can try these practice questions with the answers)

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