What is nPr and nCr in math

In Maths, nPr and nCr are the probability functions that represent permutations and combinations. The formula to find nPr and nCr is:

  • nPr = n!/(n-r)!
  • nCr = n!/[r! (n-r)!]

Here n! is the product of all positive integers less than and equal to n.

For example, if n = 5, then n! = 5 x 4 x 3 x 2 x 1

The method of representation of a group of objects and arranging them in various ways, is described by permutations and combinations

Permutation: nPr represents the probability of selecting an ordered set of ‘r’ objects from a group of ‘n’ number of objects. The order of objects matters in case of permutation. The formula to find nPr is given by:

nPr = n!/(n-r)!

Combination: nCr represents the selection of objects from a group of objects where order of objects does not matter. 

nCr = n!/[r! (n-r)!]

Where n is the total number of objects and r is the number of selected objects.

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