Permutation and combination

Permutation:  A set of objects in which position (or order) is important. To a permutation, the trio of Brittany, Alan and Greg is DIFFERENT from Greg, Brittany and Alan.  Permutations are persnickety (picky). Combination:  A set of objects in which position (or order) is NOT important. To a combination, the trio of Brittany, Alan and Greg is THE SAME AS Greg, Brittany and Alan.                         Let's look at which is which: Permutation       versus       Combination 1. Picking a team captain, pitcher, and shortstop from a group. 1. Picking three team members from a group. 2.  Picking your favorite two colors, in order, from a color brochure. 2.  Picking two colors from a color brochure. 3.  Picking first, second and third place winners. 3.  Picking three winners.

Formulas:

A permutation is the choice of r things from a set of nthings without replacement and where the order matters.
Special Cases:
A combination is the choice of r things from a set of nthings without replacement and where order does notmatter.  (Notice the two forms of notation.)
Special Cases:

  

Example 1: 
Evaluate  :
                       

Notice how the cancellation occurs, leaving only 2 of the factorial terms  in the numerator.  A pattern is emerging ... when finding a combination  such as the one seen in this problem, the second value (2) will tell you  how many of the factorial terms to use in the numerator, and the  denominator will simply be the factorial of the second value (2).