Permutations
A permutation is an ordered arrangement.
- The number of ordered arrangements of r objects taken from n unlike objects is:
nPr = n! .
(n – r)!
Example
In the Match of the Day’s goal of the month competition, you had to pick the top 3 goals out of 10. Since the order is important, it is the permutation formula which we use.
10P3 =10!
7!
= 720
There are therefore 720 different ways of picking the top three goals.
Probability
The above facts can be used to help solve problems in probability.
Example
In the National Lottery, 6 numbers are chosen from 49. You win if the 6 balls you pick match the six balls selected by the machine. What is the probability of winning the National Lottery?
The number of ways of choosing 6 numbers from 49 is 49C6 = 13 983 816 .
Therefore the probability of winning the lottery is 1/13983816 = 0.000 000 071 5 (3sf), which is about a 1 in 14 million chance.
…. তে ক্লিক কর।