Fundamental Counting Principle
When making a number of separate decisions, multiply the number of ways to make each individual decision in order to find the number of ways to make all of the decisions. Given a choice of 3 candidates for President and 2 candidates for Treasurer, there are 3*2 = 6 possible combinations for the President – Treasurer team.
Factorial (!)
The symbol for factorial is the exclamation point (!). n! is the product of all integers less than or equal to n. 4! = 4 * 3 * 2 * 1 = 24. In practice, the number 1 can be ignored (because 1 multiplied by anything does not change the product).
Combination
A subset of items chosen from a larger pool in which the order of items does not matter. When choosing 5 people from a pool of 10 to be on a basketball team, it doesn’t matter if Juliette is chosen first and Susie is chosen second or vice versa; if they are both chosen, in any order, then both are part of that 5-person team. The formula is n! / [(n - r)! * r!], where n is the total number of items in the pool and r is the number of items to be chosen. In the above example, n = 10 and r = 5.
Permutation
A subset of items chosen from a larger pool in which the order of items does matter. Ten people are running a race and three ribbons are to be awarded to the first (blue), second (red), and third (yellow) place finishers. If Juliette finishes first and Susie finishes second, this is a different scenario than Juliette finishing second and Susie finishing first; they are going to receive different ribbons depending upon how they finish! The formula is n! / (n - r)!, where n is the total number of items in the pool and r is the number of items to be chosen. In the above example, n = 10 and r = 3.
