Definition: A permutation is a set of objects that are arranged in a certain order, where the order is important.
n is the total number of objects ; r is the number of objects chosen .
You want to know how many orders your cd player will play your 13 song cd, on shuffle mode. At first there is a one in fourteen chance that any song will be played. The next song only has 1 in 12 chance of being played, because there are only 13 songs left to be played. The possibility of outcomes of a song being played decreases by one each time. The following will be the used formula.
P(n) = 13!
P(n) = 13*12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 =6227020800 ways of playing the same CD, in different orders.
Number 2 (from Webct learning)
How many five-letter "words" can be made from the alphabet if no letters are repeated? A "word" in this case is any five-letter arrangement with all letters different.
Solution:We will use the formula to answer this question.
The value of 'n' is 26 (there are 26 objects to choose from) and the value of 'r' is 5 (we pick five letters).
The formula may be convenient to use, but it is not essential. You can always find the number of arrangements (permutations) by multiplication as shown below.