Permutations and Combinations

• Recall the counting principle
• Discuss the fill in the blank method, Passwords.
• A permutation is an ordered arrangement of a set of objects
• n! = n*(n-1)*(n-1)...*2*1 if n> 0, 0!= 1
• There are n! permutations of n items.
• When selecting r items from n items _nP_r = n!/(n-r)!
• If duplicate items are involved, the number of permutations is n!/(n₁!n₂!...n_r!)
• Do some exercises page 695-698
• A combination is a distinct group of objects without regard to their arrangement.
• _nCr = n!/[(n-r)!r!]
• Do some problems P 702-704
• Do some problems P 707 - 709