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Product Rule
3 shirts and 2 trousers: 6 outfits. A 4-digit PIN with digits 0-9 and repetition allowed: 10^4. Without repetition: 1098*7 for a 4-digit code from 10 digits (if leading zero allowed — read the question).
Choose Your Level
Product Rule
What is it?
3 shirts and 2 trousers: 6 outfits. A 4-digit PIN with digits 0-9 and repetition allowed: 10^4. Without repetition: 1098*7 for a 4-digit code from 10 digits (if leading zero allowed — read the question).
In simple words
- 3 shirts and 2 trousers: 6 outfits.
- m * n
- Three meals: 322
- State the rule, show the working, and check the answer.
Important terms
PRODUCT RULE: 3 shirts and 2 trousers: 6 outfits. A 4-digit PIN with digits 0-9 and repetition allowed: 10^4. Without repetition: 1098*7 for a 4-digit code from 10 digits (if leading zero allowed — read the question).
PRODUCT RULE: 3 shirts and 2 trousers: 6 outfits.
What you should learn
- State the rule or meaning of product rule in easy words.
- Apply product rule in a clear step-by-step solution.
- Check the conditions, working, and final answer for accuracy.
Examples
- m * n
- Three meals: 322
- Repetition: same n each time
MAIN IDEA
3 shirts and 2 trousers: 6 outfits. A 4-digit PIN with digits 0-9 and repetition allowed: 10^4. Without repetition: 1098*7 for a 4-digit code from 10 digits (if leading zero allowed — read the question).
EXAM USE
Write the rule first: 3 shirts and 2 trousers: 6 outfits. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Recommended for Class 11
Full school-level explanation
3 shirts and 2 trousers: 6 outfits. A 4-digit PIN with digits 0-9 and repetition allowed: 10^4. Without repetition: 1098*7 for a 4-digit code from 10 digits (if leading zero allowed — read the question).
Understand the idea, then apply it:
WHAT — PRODUCT RULE
3 shirts and 2 trousers: 6 outfits. A 4-digit PIN with digits 0-9 and repetition allowed: 10^4. Without repetition: 1098*7 for a 4-digit code from 10 digits (if leading zero allowed — read the question).
WHY — Why it matters
This rule is a separate learning unit inside fundamental principle of counting. It can be defined, applied, and checked in its own FBISE question.
HOW — How to answer
Write the rule first: 3 shirts and 2 trousers: 6 outfits. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
MAIN IDEA
3 shirts and 2 trousers: 6 outfits. A 4-digit PIN with digits 0-9 and repetition allowed: 10^4. Without repetition: 1098*7 for a 4-digit code from 10 digits (if leading zero allowed — read the question).
Remember
- multiply stages
Examples
- m * n
- Three meals: 322
- Repetition: same n each time
EXAM USE
Write the rule first: 3 shirts and 2 trousers: 6 outfits. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Remember
- focused answer
- accurate support
Examples
- State the central idea
- Use one accurate detail
- Check the final response
How to answer a product rule question
How it works
- Read the exact command word and identify what the question asks.
- State the matching idea, rule, or meaning before adding detail.
- Use the unit evidence or mathematical working that directly supports the answer.
- Check accuracy, relevance, and answer length before finishing.
Remember
- multiply stages
- independent 'and' -> multiply
- disjoint 'or' -> add
- and multiplies
- multiply stages
- focused answer
- accurate support
- multiply stages
Deeper understanding
Go beyond memorising Product Rule. Connect the definition to reasons, relationships, exceptions, and exam wording.
Common mistakes
Exam focus
Core Idea
What to Know
Example or Evidence
How to Answer
Exam focus
Quick revision
- multiply stages
- independent 'and' -> multiply
- disjoint 'or' -> add
- and multiplies
- PRODUCT RULE: 3 shirts and 2 trousers: 6 outfits. A 4-digit PIN with digits 0-9 and repetition allowed: 10^4. With
- PRODUCT RULE: 3 shirts and 2 trousers: 6 outfits.
'And' of independent choices multiplies. Adding 4+3 would be a different question.
For long answers on Product Rule: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- multiply stages
- independent 'and' -> multiply
- disjoint 'or' -> add
- and multiplies
Important formulas
- multiply stages
- independent 'and' -> multiply
- disjoint 'or' -> add
Common exam traps
- 'And' of independent choices multiplies. Adding 4+3 would be a different question.
- Do not choose a formula before checking that its conditions fit the question.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
'And' of independent choices multiplies. Adding 4+3 would be a different question.
- Mistake
Do not choose a formula before checking that its conditions fit the question.
- Mistake
Do not hide sign changes, restrictions, or skipped algebra steps.
- Mistake
'And' of independent choices multiplies. Adding 4+3 would be a different question.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
multiply stages
independent 'and' -> multiply
disjoint 'or' -> add
and multiplies
3 shirts and 2 trousers: 6 outfits. A 4-digit PIN with digits 0-9 and repetition allowed: 10^4. Without repetition: 1098*7 for a 4-digit code from 10 digits (
- Definition
- 3 shirts and 2 trousers: 6 outfits. A 4-digit PIN with digits 0-9 and repetition allowed: 10^4. Without repetition: 1098*7 for a 4-digit code from 10 digits (
- Example
- m * n
- Critical warning
- 'And' of independent choices multiplies. Adding 4+3 would be a different question.
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Exam Practice
Define
Q1. Define Product Rule.
Explain
Q2. Explain: MAIN IDEA.
Example
Q3. Give one clear example of Product Rule and say why it fits.
Mistake
Q4. State one common mistake students make about Product Rule.
Exam note
Q5. Write a short exam note on Product Rule: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.