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Arrange Combined Calculators

Online arrangement P(n, r) with the group C(n, r) Probability Statistics Tool

P(n, r) = n! / (n - r)!
Order of r elements from n different elements (consider order)
C(n, r) = n! / (r! * (n - r)!)
Number of combinations of r elements from n different elements (without order)
n! = n * (n-1) * ... * 1
n Full order of different elements
n! / (n1! * n2! * ... * nk!)
An array of duplicate elements. Enter the total number of entries and the number of duplicate categories
(n - 1)!
n. Form a circle of different elements
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Enter the value.

Arranged: Count art in probability statistics

In probabilistic and combination mathematics, ranking and integration are core concepts of how things are chosen. Whether it is calculating the probability of winning a lottery, designing complex system passwords or assigning team tasks, accurate counting is the basis for scientific decision-making.

Difference between the Permutation and the Combination

The key to distinguishing between them is... Order ：

  • Order Matters: If the order of selection of elements produces different results, the ranking is used. For example, two persons are selected from three to serve as team leaders and vice-leaders, while A is team leader B is deputy team leader and B is team leader A is in two different ranks.
  • Order Doesn't Metter: If the order is not important, it is only about which elements are selected, and the combination is used. For example, two persons were selected from three to form an interest group, which is the same as the BA team.

Core formula resolution

  • Arrange P(n, r): n! / (n - r)! 。 is the order of the r to be taken from n different elements.
  • Group C (n, r): n! / (r! * (n - r)!) 。 Compare the order of the grouping to require additional division by r! To eliminate duplications due to sequencing.
  • Factorial n: is the product of all positive integers less than or equal to n. It is the most basic operator for combining mathematics.

Advanced application scene

In addition to the underlying P and C, this tool supports more complex calculations:

  1. Multiple Arrangement: When elements have the same item (e.g. full order of the word MISISSIPPI), the factor multiplier for the duplicate item is deducted.
  2. Round-table: When elements are enclosed in a circle, the ranking is usually given because of the rotation symmetry (n-1)! 。 If a necklace or a bracelet is available, it needs to be divided by two, as it can be reversed.
  3. Allows the choice of repeat: When the same element can be selected repeatedly, the mode of counting changes (e.g. n^r ）。

How to use this tool?

You just have to select the top functionality label according to your needs and enter the corresponding one. n (total) and r (sniffs). Tools will automatically process supervalues based on BigInt (over 16) in bits) and show you the detailed calculation steps to ensure that the results are accurate. Click the Allows repetition option to switch to a calculation mode containing duplicate elements.