definitions of permutation and combination

permutation

• An ordered subset is called a permutation.
• The number of permutations of size $k$ that can be formed from the $n$ individuals or objects in a group will be denoted by $P_{k,n}$

combination

• An unordered subset is called a combination.
• One way to denote the number of combinations is $C_{k,n},$
  • but we shall instead use notation that is quite common in probability books: $\left(\begin{array}{l}n\\ k\end{array}\right),$
  • read ” $n$ choose $k$ .”