Permutations – Special Cases

1. Permutations – Special Cases M408 Probability Unit

2. Example 1 – a.) How many unique ways are there to arrange the letters PIG? b.) How many unique ways are there to arrange the letters BOO?

3. To arrange ‘n’ items with ‘p’ repeats of one type, possibly ‘q’ repeats of another type, possibly others,…use

4. Example 2 – How many ways can you arrange the letters of… a.) ATTRACTIVE b.) MISSISSIPPI

5. Example 3 – How many ways can you arrange 5 red flags and 8 white flags in a line?

6. Example 4 - How many unique ways can you arrange 5 people {A,B,C,D,E} in a circle (as opposed to a line)? How would you name this arrangement? ABCDE BCDEA CDEAB DEABC EABCD These 5 ‘arrangements’ are all the same when you arrange the items in a circle!

7. Circular Permutations For ‘n’ objects in a circular arrangement, there are or (n-1)! Permutations.

8. Example 5 - How many ways are there to arrange 9 people at a rectangular table?

9. Reference Points – Not all circular arrangements have circular permutations. If one position in the arrangement is ‘special’, we treat it as a starting point. If there is a clear reference (starting) point, then the arrangement is considered linear.

10. Example 6 - How many ways are there to arrange 9 people at a rectangular table that has one really fancy chair?

11. Reflection Principle Applies to arrangements that can be turned over and viewed from a different perspective (bracelets, beaded necklaces, etc.) If an arrangement is reflective, divide your answer by 2.

12. Example 7 - How many ways can you arrange 6 beads on a bracelet? These two arrangements are the same in a flipped object.

13. Example 8 - How many ways can you arrange 6 beads on a bracelet that has a clasp?