MathematicsChapter 6: Permutation and Combination
Factorial Values and Recursion
1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720.
Learning objectives
- State the rule or meaning of factorial values and recursion in easy words.
- Apply factorial values and recursion in a clear step-by-step solution.
- Check the conditions, working, and final answer for accuracy.
Definition
1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720. n! = n * (n-1)!. A calculator n! button is fine in a paper that allows it; still show a cancel line in algebra.
Where / symbols
- FACTORIAL VALUES AND RECURSION
- 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720. n! = n * (n-1)!. A calculator n! button is fine in a paper that allows it; still show a cancel line in algebra.
- VALUES
- 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720.
Relationship
- n! = 12...*n
- 0! = 1
Overview
Understand the idea, then apply it:
Main Idea
1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720. n! = n * (n-1)!. A calculator n! button is fine in a paper that allows it; still show a cancel line in algebra.
Examples 6! = 6*5! · 10! huge · 0! = 1 not 0
Exam Use
Write the rule first: 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720. 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 — FACTORIAL VALUES AND RECURSION
1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720. n! = n * (n-1)!. A calculator n! button is fine in a paper that allows it; still show a cancel line in algebra.
WHY — Why it matters
This rule is a separate learning unit inside factorial n!. It can be defined, applied, and checked in its own FBISE question.
HOW — How to answer
Write the rule first: 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
How to answer a factorial values and recursion 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
0! = 1. If you put 0, nCr formulas break at r=0.
Key points
- build from smaller
- n! = 12...*n
- 0! = 1
- focused answer
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Factorial Values and Recursion
Sticky Notes · Quick Revision
Core Idea
- 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720.
What to Know
- 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720. n! = n * (n-1)!. A calculator n! button is fine in a paper that allows it; still show a cancel line in algebra.
Example or Evidence
- 6! = 6*5!
- 10! huge
- 0! = 1 not 0
How to Answer
- Write the rule first: 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Common Error
- 0! = 1. If you put 0, nCr formulas break at r=0.
FBISE Exam Check
- State the rule, show the working, and check the answer.
60-second revision
- 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720.
- 6! = 6*5!
- 10! huge
- State the rule, show the working, and check the answer.
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