Combinatorial counting

📄️ Sampling with replacement

Let us consider two examples.

📄️ Sampling without replacement

Let us revisit Benjawan's example. Let us say that she wants to buy different types of chocolates for the four best performing students in this class. Now the number of possibilities should be $10\cdot 9 \cdot 8 \cdot 7$ instead of $10^4$.

📄️ Permutations

An important object in discrete mathematics is called permutation - a bijective mapping between set $X$ and itself. From Theorem 24, there are a total of $n!$ permutations on a set $X$ of size $n$.