Advanced Combinations and Permutations From 10 people, 6 are male and 4 are female. How many ways can you select a group of 3 people? Create a group of 3 people comprising only females? Create a group of 3 people with 2 males and 1 female?

Combining combinations and permutations We multiply combinations and permutation when we have complex events, like the previous problem. All of the “r’s” in the nCr or nPr formulas should add to the total number of selections.

Arrangements with repeats How many ways can 6 books be arranged on a shelf? 6! = 720 How many unique arrangements are there if 3 books are the same? 6! 3! = 6×5×4×3! 3! =120

Arrangements continued When arrangements have identical elements that repeat, we divide by the number of each-non-unique item factorial. How many unique was can the letters in the word “supplies.” There are 8 letters, but two of them occur twice, so… 8! 2!×2!