This document defines probability as a measure between 0 and 1 of the likelihood of a future event occurring. It can be calculated using formulas. An event with a probability of 0 is impossible and will never happen, while an event with a probability of 1 is certain and will definitely happen. Examples are provided to demonstrate calculating probabilities of outcomes from dice rolls or seating arrangements. The document also defines permutations as arrangements that consider order important, and provides a formula to calculate permutations. Combinations are defined as arrangements that do not consider order, and a different formula is given to calculate combinations.

1. DEFINITION:
A probability is a measure of the likelihood that an event in the
future will happen. It can only assume a value between 0 and 1.
It can be calculate by using the following formula:

2. If the probability of an event occurring is 0, then it is an
impossible event means it will never happen.
If the probability of an event occurring is 1, then it is a
certain event, means it will definitely happen.

3. EXAMPLE:
six faced cubical dice is thrown once, what is the probability of
getting an even number?
SOLUTION:
Number of possible outcomes= 6 {1, 2, 3, 4, 5, 6}
Number of targeted outcomes (even numbers)= 3 {2, 4, 6}

5. If an operation can be performed in n1 ways, if for each of
these a second operation can be performed in n2 ways,
third operation can be performed in n3 ways and so on,
then the sequence of k operations can be performed in
n1.n2. n3…..nk ways.
P = n1 × n2 × n3…. nk
Note:
Every event should be different or independent with each other.

6. EXAMPLE:
There are three boys in a class. In how many ways
they can sit if there is no restrictions?
SOLUTION:
P= n1 × n2 × n3
P= (3) (2) (1)
P= 6 ways.

8. A permutation is any arrangement of r objects selected from
n possible objects. The order of arrangement is important in
permutations.
The formula for calculating permutation is:

9. EXAMPLE:
2 markers are drawn from 3 markers. Find the number of
permutations that can be possible?
SOLUTION:
n=3
r= 2
The total number of sample points is

11. A combination is the number of ways to choose r objects
from a group of n objects without regard to order.
Because the order of the subgroup doesn’t matter, the
combination solutions will be fewer than the permutation
solutions and will be expressed by the following formula:

12. EXAMPLE:
From 4 Republicans and 3 Democrats find the number of
committees of 3 that can be formed with 2 Republican and 1
Democrat.
SOLUTION:
The number of ways of selecting 2 Republicans from 4 is