Probability and Statistics: Covers probability theory, random variables, distributions, and data interpretation.
Calculus: Focuses on differentiation, integration, limits, continuity, and partial derivatives.
Linear Algebra: Involves matrices, determinants, vector spaces, eigenvalues, and eigenvectors.
Understanding the Basics of Counting is crucial before diving into probability and combinatorics.
When dealing with selections or arrangements, we use two fundamental principles: Addition and Multiplication.
If a task can be done in ‘m’ ways and another task can be done in ‘n’ ways, and only one task is to be performed, the total number of ways is:
m+n
When you feel the following keywords occur in the question:
either one task,
or another task,
only one option, then apply the Addition Principle.
If a task can be done in ‘m’ ways and after that another task can be done in ‘n’ ways, then the total number of ways to perform both tasks is:
m×n
When you feel the following keywords occur in the question:
and,
both,
all tasks together, then apply the Multiplication Principle.
Let’s practice with some simple real-world examples:
Question:
There are 5 boys and 7 girls in a class. In how many ways can we select a boy and a girl?
Solution:
Since the task involves both boy and girl, we multiply:
5×7=35 ways
Question:
There are 5 boys and 7 girls in a class. In how many ways can we select a boy or a girl?
Solution:
Since it’s a choice between a boy or a girl, we add:
5+7=12 ways
Question:
You have 3 shirts and 4 trousers. How many ways can you dress by selecting one shirt and one trouser?
Solution:
Feeling of both shirt and trouser → Multiplication:
3×4=12 ways
Question:
A student can choose either Mathematics (5 options) or Physics (4 options) as an elective. How many ways can the choice be made?
Solution:
Feeling of either one subject → Addition:
5+4=9 ways
In this introductory blog on Engineering Mathematics, we:
Explored the syllabus structure.
Understood the Fundamental Principle of Addition and Multiplication.
Solved simple examples for clarity.
Mastering these basic counting concepts is crucial before moving ahead to permutations, combinations, and advanced probability.
Stay tuned for the next topic: Permutations and Combinations Simplified!