Probability and combinatorics

Combinatorics answers the question “in how many ways?”. Key notions:

$P_n=n!\qquad V_n^k=\frac{n!}{(n-k)!}\qquad C_n^k=\binom{n}{k}=\frac{n!}{k!(n-k)!}$

Permutations are orderings of all $n$ items, arrangements — a choice of $k$ out of $n$ taking order into account, combinations — without order. The calculator also works out arrangements with repetition $n^k$.

In the second mode you can compute classical probability: $P(A)=\dfrac{|A|}{|\Omega|}$ — the ratio of favourable outcomes to all equally likely ones, together with the probability of the complementary event $P(A')=1-P(A)$.