A
permutation is a sequence of elements in which no element appears twice. In a sequence, unlike in a
set, the order in which the elements are written down matters. Suppose you have a total of
n distinct objects at your disposal and you want to create permutations of
k elements selected from those
n, where
k≤
n.
In how many ways can that be done?
- We can select the first member of the list in n ways because there are n distinct elements.
- The second member of the list can be filled in (n-1) ways since we have used up one of the n elements already.
- The third member can be filled in (n-2) ways since 2 have been used already.
- This pattern continues until there are k names on the list. This means that the last member can be filled in (n-k+1)'' ways.
Summarizing, we find that a total of
- n * (n-1) * (n-2) * ... * (n-k+1)
different permutations of
k objects, taken from a pool of
n objects, exist. If we denote this number
by
nP
k and use the
factorial notation, we can write
- nPk = n! / (n-k)!
See also
Combinations.
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