Elementary combinatorics

   The art of counting is called  combinatorics. Here is a short listing of the formulas. All are the consequences of the product rule of counting.

Permutations: 
Permutation is an arrangement (ordering) of k out of n distinct objects without repetitions. The number of permutations is . In particular, the number of ways to order n objects is n!

Combinations:  
Combinations are k-element subsets of n distinct elements. The number of combinations is .

Variations: 
Variations are arrangements of k out of n distinct objects with repetitions allowed. The number of variations is