Ch 5Permutations and Combinations — Class 12 Mathematics, concept-first.

Suppose you have a suitcase secured by a number lock with 4 wheels, each showing the digits 0 through 9.

Consider a simple wardrobe problem. Mohan has 3 pants and 2 shirts. How many different pant-shirt combinations can he wear?

When you arrange objects in a specific order, each distinct ordering is called a permutation. The key point is that order matters.

When we talk about permutations, we are asking: In how many ways can we arrange a given set of objects? The simplest case — and the one that builds the foundation for everything else — is when every o…

The product of the first natural numbers is given a compact symbol: , read as "n factorial".

The earlier formula for the number of permutations of different objects taken at a time was a product of decreasing factors:

Until now, every permutation problem we solved assumed that all objects being arranged were different from one another.

When you pick a team, the order in which you name the players does not matter. A team of X and Y is the same as a team of Y and X.

- The fundamental principle of counting (multiplication rule): if one event can occur in ways and another independent event in ways, the two together can occur in ways.

Higher-order thinking / exemplar-style practice problems.