Chapter 7 of 7

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Tamil Nadu (TNBSE)Class 8 Mathematics★ 3-6 marks in the TN Class 8 annual exam through MCQs and counting/logical-reasoning problems

Information Processing

Samacheer Kalvi (TN State Board) Class 8 Maths Chapter 7, Information Processing. Systematic and repeated counting, the principle of counting (rule of product), tree diagrams, and step-by-step algorithmic thinking for puzzles like efficient packing and shortest routes. Notes with worked examples, common mistakes, book-back practice and quick revision.

⏱ 16 min readEasy difficulty✓ Free · NCERT-aligned

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By the end of this chapter you'll be able to…

1Count possibilities systematically
2Apply the rule of product
3Use tree diagrams to list outcomes
4Follow step-by-step algorithms
5Solve simple counting puzzles

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Why this chapter matters

Information Processing builds logical and computational thinking — systematic counting, the rule of product and algorithmic problem-solving. These skills support reasoning across maths and computer science and give easy marks in the TN Class 8 exam.

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Class 7 — Logical reasoning

Patterns and organised listing.

Information Processing — Class 8 Maths (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 8 Mathematics, Chapter 7 (the final chapter). Thinking systematically to count and organise.

1. About this chapter

This chapter develops logical and computational thinking — systematic counting, the principle of counting, tree diagrams, and step-by-step (algorithmic) methods for solving puzzles.

2. Systematic and repeated counting

List possibilities in an organised way so that none is missed and none is repeated.
Repeated counting (iteration) applies the same step again and again until the task is complete.

3. Principle of counting

Rule of product: if one task can be done in m ways and another in n ways, then both together can be done in m × n ways.
Tree diagrams show all the possible choices branch by branch.

4. Algorithmic thinking

An algorithm is a clear, step-by-step procedure to solve a problem (used in packing, shortest-route and arrangement puzzles).
Breaking a problem into ordered steps makes it easier and avoids mistakes.

5. Worked examples

Example 1. A girl has 3 shirts and 2 skirts. How many different outfits can she make? By the rule of product: 3 × 2 = 6 outfits.

Example 2. How many 2-digit numbers can be formed using the digits 1, 2, 3 (repetition allowed)? 3 × 3 = 9 numbers.

Example 3. Why use a tree diagram? To list all possibilities clearly so that none is missed.

6. Common mistakes

Mistake: Counting some possibilities twice. Fix: Count systematically (in order) so nothing repeats.
Mistake: Adding instead of multiplying choices. Fix: For independent choices, multiply (rule of product).
Mistake: Skipping steps in a procedure. Fix: Follow the algorithm step by step.

7. Practice (book-back style)

State the rule of product (principle of counting).
A menu has 4 starters and 3 main dishes. How many starter–main combinations are there?
How many 2-digit numbers can be formed from 5, 6, 7 (repetition allowed)?
What is a tree diagram used for?
What is an algorithm?

8. Answer key

If one task can be done in m ways and another in n ways, both can be done in m × n ways.
4 × 3 = 12 combinations.
3 × 3 = 9 numbers.
To list all possible outcomes clearly so none is missed.
A clear, step-by-step procedure to solve a problem.

9. Quick revision

Chapter 7 (final) · systematic counting, principle of counting, algorithms.
Count systematically — none missed, none repeated.
Rule of product: m ways × n ways = m × n ways.
Tree diagrams list all possibilities.
Algorithms solve problems step by step.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Rule of product

m ways × n ways = m × n ways

For independent choices.

Systematic counting

list in order — none missed, none repeated

Avoids double counting.

Algorithm

a clear step-by-step procedure

Used for puzzles and tasks.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Counting some possibilities twice

✓ Count systematically (in order) so nothing repeats.

WATCH OUT

✗ Adding instead of multiplying choices

✓ For independent choices, multiply (rule of product).

WATCH OUT

✗ Skipping steps in a procedure

✓ Follow the algorithm step by step.

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

Multiple choice questions

MCQs on counting and logical reasoning.

Questions

Counting problems

Rule of product and tree diagrams.

Questions

Algorithm puzzles

Step-by-step packing and route problems.

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· Concept

State the rule of product (principle of counting).

▶ Show solution

If one task can be done in m ways and another in n ways, both together can be done in m × n ways.

Q2EASY· Counting

A menu has 4 starters and 3 main dishes. How many starter–main combinations are there?

▶ Show solution

4 × 3 = 12 combinations.

Q3EASY· Counting

How many 2-digit numbers can be formed from 5, 6, 7 (repetition allowed)?

▶ Show solution

3 × 3 = 9 numbers.

Q4EASY· Concept

What is a tree diagram used for?

▶ Show solution

To list all possible outcomes clearly so that none is missed.

Q5EASY· Concept

What is an algorithm?

▶ Show solution

A clear, step-by-step procedure to solve a problem.

Q6EASY· Counting

A girl has 3 shirts and 2 skirts. How many outfits can she make?

▶ Show solution

3 × 2 = 6 outfits.

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Chapter 7 (final) of Samacheer Kalvi Class 8 Mathematics.
•Count systematically — none missed, none repeated.
•Rule of product: m ways × n ways = m × n ways.
•Tree diagrams list all possibilities.
•Algorithms solve problems step by step.
•Multiply (not add) independent choices.

Tamil Nadu (TNBSE) marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: 3-6 marks across MCQ and counting problems

Question type	Marks each	Typical count	What it tests
MCQ	1	1-2	Counting and reasoning
Counting	2	1-2	Rule of product, tree diagrams
Puzzle	2	0-1	Step-by-step procedures

Prep strategy

List possibilities in order
Multiply independent choices
Draw tree diagrams for clarity
Solve puzzles step by step

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Planning

Counting combinations helps plan menus, routes and schedules.

Computer science

Algorithmic thinking is the basis of programming.

Logistics

Packing and shortest-route puzzles model real delivery problems.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

Count in a fixed, systematic order
Use the rule of product for combined choices
Draw a tree diagram when unsure
Write the steps of the procedure clearly

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

Count the number of routes on a grid from corner to corner.
Design an algorithm to sort five numbers.

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

TN Class 8 Annual ExamMedium

Foundation / NMMS reasoningMedium

School unit testsHigh

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Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

Multiply when choices are made together and are independent (rule of product); add when choosing between separate, mutually exclusive options.

It branches out every choice at each step, so you can see and count all possible outcomes without missing or repeating any.

Practice more, ask doubts, find a tutor

Tamil Nadu (TNBSE) Class 8 mock tests

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Mathematics flashcards

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