Combinatorics and Probability

In probability theory, there are many applications of combinatorics. For example, when we find the probability of occurrence of a particular event A, we can use the below formula:

P(A) = Probability that A occurs = Number of outcomes where A happen/Total number of possible outcomes

We can also use combinatorics to calculate the total number of possible outcomes.

Example 4: Four students namely P, Q, R, and S sit randomly at four corners of the classroom while playing a game. Find the probability that Q sits at the North-east corner of the room.

Solution:
We know that there are 24 ways that a student can sit at four corners. Also, there are 6 (i.e. 3! ways) possible ways that Q can sit at the North-east corner.
Therefore, the probability that Q sits at the North-east corner of the room
= Number of ways that Q can sit at the North-east corner/Total number of ways
= 6/24 = 1/4