MathematicsChapter 6: Permutation and Combination
Product Rule
3 shirts and 2 trousers: 6 outfits.
Learning objectives
- 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.
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 (if leading zero allowed — read the question).
Where / symbols
- PRODUCT RULE
- 3 shirts and 2 trousers: 6 outfits. A 4-digit PIN with digits 0-9 and repetition allowed: 10^4. Without repetition: 10*9*8*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.
Overview
Understand the idea, then apply it:
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).
Examples m * n · Three meals: 3*2*2 · 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.
Examples State the central idea · Use one accurate detail · Check the final response
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.
How to answer a product rule question
- 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.
In simple words
'And' of independent choices multiplies. Adding 4+3 would be a different question.
Key points
- multiply stages
- independent 'and' -> multiply
- disjoint 'or' -> add
- focused answer
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Product Rule
Sticky Notes · Quick Revision
Core Idea
- 3 shirts and 2 trousers: 6 outfits.
What to Know
- 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).
Example or Evidence
- m * n
- Three meals: 322
- Repetition: same n each time
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.
Common Error
- 'And' of independent choices multiplies. Adding 4+3 would be a different question.
FBISE Exam Check
- State the rule, show the working, and check the answer.
60-second revision
- 3 shirts and 2 trousers: 6 outfits.
- m * n
- Three meals: 322
- State the rule, show the working, and check the answer.
Did you understand this topic?
Your answer is saved with your learning record. It does not mark the topic as mastered.