If there are n different objects, the number of permutations is factorial n which is also written as n! and is equal to 1*2*3*...*(n-1)*n.
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The number of R-combinations in a set of N objects is C= N!/R!(N-R)! or the factorial of N divided by the factorial of R and the Factorial of N minus R. For example, the number of 3 combinations from a set of 4 objects is 4!/3!(4-3)! = 24/6x1= 4.
The objects within a number set can be caled as "Elements" or "members".
In group theory, an alternating group is a group of even permutations of a finite set.