Permutations And Combinations: quiz

Permutations (ordered selection without repetition)

Combinations (unordered selection)

Binomial coefficient identities (symmetry and Pascal)

Circular permutations (distinct objects around a circle)

Derangements (no fixed point permutations)

Stars and bars (non-negative integer solutions)

Multinomial coefficient (ordered partition of distinct objects)

Combinations with repetition (multiset selection)

Distributing distinct objects to distinct boxes (functions)

Positive compositions (each part at least 1)

Necklace / bracelet (rotations and reflections)

Vandermonde’s identity (convolution of binomials)

Circular permutations (distinct objects)

Permutations of multiset $\frac{n!}{p!q!r!}$

Derangements $!n$

Combinations ${}^n C_r$

Symmetry ${}^n C_r = {}^n C_{n-r}$

Stars and bars (non-negative integers)

Multinomial coefficient

Multiplication principle of counting

Permutations ${}^n P_r$

Permutations with repetition $n^r$