Permutations: Mastering Order in A-Level Statistics
In A-Level Statistics (9709), a Permutation is simply an arrangement of items where order matters. If swapping the position of two people changes the outcome, you are dealing with permutations.
1. Linear Arrangements ($n!$)
If you have 5 different books and want to arrange them all on a shelf, the number of ways is $5!$ (5 factorial).
2. Arranging $r$ items from $n$ distinct objects
When you only need to pick and arrange a subset (e.g., picking a President and Secretary from a group of 10), use the $^nP_r$ formula:
3. The "Identical Items" Rule
When some items are the same (like the letters in 'RECURR'), we divide to remove duplicate arrangements.
Calculation: $5! / 2! = 60$ ways.
4. Constraint Strategies for Exams
The "Tie" Method (Items Together)
If two people must sit together, treat them as a single block. Don't forget to multiply by the internal arrangements of that block!
The "Gap" Method (Items Apart)
If items must NOT be together, arrange the others first and place the restricted items in the spaces between them.
