The solution of tasks on finding of various combinations is of genuine interest, and the combination theory is applied in many fields of science, for example, in biology to interpretation of the DNA code or at sports competitions to calculation of number of games between participants.
It is required to you
- calculator
Instruction
1. Shifts without repetitions are such combinations from n-go of quantity of various elements in which the quantity of elements remains to equal n, and their order changes in various ways. P(n) = 1*2*3 * …*n=n! PrimerSkolko of shifts can be made of figures 5,8,9? From n statement of the problem = 3 (three figures 5,8,9). Let's use a formula for calculation of possible number of shifts without repetitions: P _ (n) = n! Having substituted in formula n = 3, we will receive P = 3! = 1*2*3 = 6
2. Shifts with repetitions are such combinations from n-go of quantity of elements (including repeating) in which the quantity of elements remains to equal n, and their order changes in various ways.Pn = n! / n1! * n2! * … *nk! where n – total number of elements, n1, n2 … nk – quantity of the repeating elements
3. Combinations without repetitions – all this possible combinations (groups) of n of various elements on m in each group (m? n), which differ from each other only in structure of elements (groups differ from each other at least in one element). With = n! / m! (n - m)!
4. Combinations to repetitions – all this possible combinations (groups) of n of various elements on m to each group (m – any), and is allowed repetition of one element several times (groups differ from each other at least in one element) With = (n + m – 1)! / m! (n-1)!
5. Placements without repetitions – all this possible combinations (groups) of n of various elements on m in each group (m? n), which differ among themselves as structure of the elements entering into groups and their order. And = n! / (n – m)!
6. Placements with repetitions – all this possible combinations (groups) of n of various elements on m to each group (m – any) which differ among themselves as structure of the elements entering into groups and their order in which repetition of elements is also allowed. And = n^m