# Probability & Permutation

## Factorial notation

**It is a simple way of writing the product of all whole numbers up to a given number.**

**-The n factorial is defined as the product of the integers from 1 to n.**

**-It can be written as "n!". This means that we are looking for (n)(n-1)(n-2)(n-3)...(3)(2)(1)**

** N.B: **Two numbers containing factorials and being divided by one another does not mean they can be simplified:

**10!/5!=/=2!**

## Permutation ( Ordered Arrangement)

Using factorial notation: n objects can be arranged in "n!" ways.

__Theorem for number of permutations (with no repetitions):__

**nPr=n(n−1)(n−2)...(n−r+1)=n!/(n−r)!**

**When there is repetition, it is possible to assign different "n"s for each.This results in a new formula:**

**n!/n1!×n2!×n3!×...×nk!**

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## Probability

The **sample space** is the set of all possible outcomes of the experiment.The **Event (E)** is a subset of the sample space.

P(E)=r/n where r is the number of ways for a specific outcome and n is the number of all outcomes. This is to determine the success of an event or its occurrence.

To determine non-occurrence: P(E/)= 1-r/n

The sum of the probabilities in any experiment is equal to 1.

the probability of an even ranges between 0 and 1. if the event's occurrence is impossible, then the probability is 0, although absolute certainty means that the probability is 1.