The word ‘probability’ means ‘likelihood’ or ‘chance.’ While an event is likely to occur, the likelihood of that event occurring is 1, and when the event is certain not to occur, the probability of that event occurring is 0.

As a result, the likelihood value varies from 0 to 1. Various schools of thought have described probability in a variety of ways. Some of these are mentioned further down..

**Permutations and combinations**

**Permutations:**

Permutation of Object refers to any arrangement of n objects in a specific order. An r-permutation, or a permutation of n objects taken r at a time, is any arrangement of any r n of these objects in a given order.

It is denoted by the letter P. (n, r)

P (n, r)

**Theorem:** Demonstrate that the total number of permutations ofn stuff is n!

**Proof:** We know that

**Combinations:**

A combination is a collection of any or all objects from a set of given objects, with no regard for their order. nCr or C represents the number of combinations of n items taken r at a time (n, r).

**Proof:** The number of different permutations of n different items taken r at a time is given by