COMBINATORICS WORD SYMBOLS

symbol	Symbol Name	Meaning / definition	Example
n!	factorial	n! = 1⋅2⋅3⋅…⋅n	5! = 1⋅2⋅3⋅4⋅5 = 120
nPk	permutation	_{n}P_{k}=\frac{n!}{(n-k)!}	5P3 = 5! / (5-3)! = 60
nCk	combination	_{n}C_{k}=\binom{n}{k}=\frac{n!}{k!(n-k)!}	5C3 = 5!/[3!(5-3)!]=10

Art of combinations and permutations. We can get 3 combinations with 2 objects. lets suppose we have 2 objects called {A , B } , we can get 3 combinations with repetition of AA , BB and one the real combination AB .

When we have 3 objects {A,B,C) and you choose only two objects to make those combinations you will get 6 Combinations with repetition {AA,AB/BA,AC/CA,BB,BC/CB,CC } and without repetition you will get only 3 { AB/BA,AC/CA,BC/CB }