Combinatorics — permutations, combinations, placements

Elements of combinatorics–permutations, placements, combinations – as terms known to us today, are first found in the works of Jacob Bernoulli (“permutation” and “placement”) and Blaise Pascal (“combination”). At the same time, the term “combinatorics” was coined by Gottfried Wilhelm Leibniz (by the way, Bernoulli’s teacher), who talked about this field of mathematics as an art. In addition to these elements, there are other combinatorial configurations: “composition” (decomposition) and “number splitting”.

Finding the number of permutations, the number of placements, the number of combinations
k =
n =


Let the number of placements (when selecting elements without repetition) from n to k be . Then the following equality serves to determine the desired value:

When selecting with repetition (i.e., with such placement of elements), the formula is used