Combinatorial rules

With order important and no repetition, arranging n elements gives n! possibilities and assigning r distinct roles gives n!/(n − r)!. An unordered pair gives n(n − 1)/2. A code with r positions, n symbols per position and repetition allowed gives nʳ.

For successive choices joined by “and”, multiply: shirt and trousers give a × b outfits. For disjoint alternatives joined by “or”, add: bus or train gives a + b choices.

Count all unrestricted arrangements. Count the forbidden arrangements by treating A and B as one block and allowing both orders inside it. Subtract forbidden arrangements from the total.

With order important and no repetition, arranging n elements gives n! possibilities and assigning r distinct roles gives n!/(n − r)!. An unordered pair gives n(n − 1)/2. A code with r positions, n symbols per position and repetition allowed gives nʳ.

With order important and no repetition, arranging n elements gives n! possibilities and assigning r distinct roles gives n!/(n − r)!. An unordered pair gives n(n − 1)/2. A code with r positions, n symbols per position and repetition allowed gives nʳ.

With order important and no repetition, arranging n elements gives n! possibilities and assigning r distinct roles gives n!/(n − r)!. An unordered pair gives n(n − 1)/2. A code with r positions, n symbols per position and repetition allowed gives nʳ.

With order important and no repetition, arranging n elements gives n! possibilities and assigning r distinct roles gives n!/(n − r)!. An unordered pair gives n(n − 1)/2. A code with r positions, n symbols per position and repetition allowed gives nʳ.

Count unordered pairs from the first group: swapping the pair does not create a new choice. Count choices for the second-group member separately. Both selections are required, so multiply their counts.

For successive choices joined by “and”, multiply: shirt and trousers give a × b outfits. For disjoint alternatives joined by “or”, add: bus or train gives a + b choices.

For successive choices joined by “and”, multiply: shirt and trousers give a × b outfits. For disjoint alternatives joined by “or”, add: bus or train gives a + b choices.