Wednesday 22 June 2011

Permutations and Combinations

Permutation: It is an ordered arrangement of objects from a group without repetitions.

For example, there are two ways to order the boxes 12 without repeating a sequence. The two permutations are 12 and 21.

In general, the number of permutation of n items chosen k at a time is:

nPk = n!
(n − k)!




Why these are important?

If there are only two possible outcomes then permutations can be used to calculate the probability of an event in that experiment.



Combination: A selection of objects from a group, when the order of the selection does not matter. For example, the combinations of the number 123 taken two at a time are 12, 13, and 23.
The subgroups 12 and 21 are considered the same combination, because order does not matter.
In general, the number of combinations of n things taken k at a time is:

nCk  =           n!            
            (n − k)! k!

Why these are important?
In statistics, this expression is used in the formula to calculate the probability of observing k events (successes) in n trials in an experiment with only two outcomes (a binomial experiment).

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