Permutations — A/L Combined Mathematics

What must I remember about Permutations?

• Definition of Permutation: An arrangement of objects in a definite order (order of selection MATTERS).
• Permutations of n distinct objects taken r at a time: nPr = n! / (n - r)! = n(n - 1)(n - 2)...(n - r + 1); nPn = n!.
• Permutations with Identical Objects: The number of permutations of n objects where p are of one kind, q of another, and r of a third kind is n! / (p! * q! * r!).
• String / Tie method (Items always together): Treat the items that must remain together as a single block; permute the block with remaining items, then multiply by internal permutations within the block.
• Gap method (Items never together): First arrange the unconstrained items; then place the restricted items into the gaps between and at the ends of the unconstrained items.

Test yourself (1 minute)

1. Circular Permutations

   Arranging n distinct objects in a circle has (n - 1)! ways (fixing one reference position); if clockwise and counterclockwise arrangements are indistinguishable (e.g., beads on a necklace), number of arrangements is (n - 1)! / 2.

2. Complementary counting ('At least two together')

   Total arrangements without restriction MINUS arrangements where no two are together (gap method).

3. Rank of a word in dictionary

   Form permutations alphabetically by determining how many words precede the given word starting with earlier letters.

Practise Permutations questions today

Source: NIE G.C.E. (A/L) Combined Mathematics Resource Book - Pure Mathematics, Unit 23

What should I study first?

What comes next?

Next in the syllabus

Where does Permutations fit in the syllabus?

Year 2 · Term 1