Statistics: Permutations and Combinations

- Factorials are products, indicated by an exclamation mark. For example,   (Remember that 0! is defined to be equal to 1)
-  Permutations: The number of ways to choose a sample of elements from a set of distinct objects where order does matter, and replacements are not allowed.

For a permutation problem, use this formula:
 P(n,r) = n!/(n-r)

-  Combination: The number of ways to choose a sample of elements from a set of distinct objects where order does not matter, and replacements are not allowed.

For a combination problem, use this formula:
C(n, r) = P(n,r)/ r!


Examples:
Example 1.  How many ways can the first and second place be awarded to people?
Solution: Since the order matters, (the first and second place are different!) we need to use permutation formula where is 7 and is 2. Then: , remove from both sides of the fraction. Then:

Example 2.  How many ways can we pick a team of people from a group of ?
Solution: Since the order doesn’t matter, we need to use a combination formula where is 8 and is 3.
Then: