What is a permutation?
A permutation is an arrangement of items where order matters. ABC and BAC are different permutations because the order is different.
How many permutations of 5 items taken 3 at a time?
There are 60 permutations. Use the formula P(n,r) = n!/(n-r)!, so P(5,3) = 5!/(2!) = 5 × 4 × 3 = 60.
What is the difference between permutations and combinations?
In permutations, order matters: ABC differs from BAC. In combinations, order does not matter: ABC equals BAC. Permutations always count more arrangements.
Can I generate permutations where items repeat?
Yes. With repetition allowed, each item can appear multiple times in an arrangement. The formula becomes P(n,r) = n^r instead of n!/(n-r)!.
What are permutations commonly used for?
Permutations are used for scheduling, creating passwords, organizing seating charts, arranging tournament brackets, and any situation where arrangement order matters.