How do you find all the combinations of a list?

Answer 1

To find the number of combinations possible for a set of objects, we need to use factorials (a shorthand way of writing n x n-1 x n-2 x ... x 1 e.g. 4! = 4 x 3 x 2 x 1). If you have a set of objects and you want to know how many different ways they can be lined up, simply find n!, the factorial of n where n is the number of objects. If there is a limit to the number of objects used, then find n!/(n-a)!, where n is the number of objects and n-a is n minus the number of objects you can use. For example, we have 10 objects but can only use 4 of them; in formula this looks like 10!/(10-4)! = 10!/6!. 10! is 10 x 9 x 8 x ... x 1 and 6! is 6 x 5 x ... x 1. This means that if we were to write out the factorials in full we would see that the 6! is cancelled out by part of the 10!, leaving just 10 x 9 x 8 x 7, which equals 5040 i.e. the number of combinations possible using only 4 objects from a set of 10.

Answer 2

nCr = (n!)/((r!)((n-r)!))