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.
Why these are important?
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!
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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