6 min read
Not Together / Ends
Not together = n! - (together). A particular person at an end: 2 * (n-1)! for a line. Read 'at least one' as a split of cases if needed.
Choose Your Level
Not Together / Ends
What is it?
Not together = n! - (together). A particular person at an end: 2 * (n-1)! for a line. Read 'at least one' as a split of cases if needed.
In simple words
- Not together = n!
- All minus glued
- Ends: 2 choices
- State the rule, show the working, and check the answer.
Important terms
NOT TOGETHER / ENDS: Not together = n! - (together). A particular person at an end: 2 * (n-1)! for a line. Read 'at least one' as a split of cases if needed.
NOT TOGETHER / ENDS: Not together = n!
What you should learn
- State the rule or meaning of not together / ends in easy words.
- Apply not together / ends in a clear step-by-step solution.
- Check the conditions, working, and final answer for accuracy.
Examples
- All minus glued
- Ends: 2 choices
- Show both pieces
MAIN IDEA
Not together = n! - (together). A particular person at an end: 2 * (n-1)! for a line. Read 'at least one' as a split of cases if needed.
EXAM USE
Write the rule first: Not together = n! Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Recommended for Class 11
Full school-level explanation
Not together = n! - (together). A particular person at an end: 2 * (n-1)! for a line. Read 'at least one' as a split of cases if needed.
Understand the idea, then apply it:
WHAT — NOT TOGETHER / ENDS
Not together = n! - (together). A particular person at an end: 2 * (n-1)! for a line. Read 'at least one' as a split of cases if needed.
WHY — Why it matters
This rule is a separate learning unit inside restrictions in arrangements. It can be defined, applied, and checked in its own FBISE question.
HOW — How to answer
Write the rule first: Not together = n! Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
MAIN IDEA
Not together = n! - (together). A particular person at an end: 2 * (n-1)! for a line. Read 'at least one' as a split of cases if needed.
Remember
- complement
Examples
- All minus glued
- Ends: 2 choices
- Show both pieces
EXAM USE
Write the rule first: Not together = n! 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 not together / ends 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
- complement
- together: glue as one super person
- not together: all - together
- complement
- complement
- focused answer
- accurate support
- complement
Deeper understanding
Go beyond memorising Not Together / Ends. 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
- complement
- together: glue as one super person
- not together: all - together
- NOT TOGETHER / ENDS: Not together = n! - (together). A particular person at an end: 2 * (n-1)! for a line. Read 'at least
- NOT TOGETHER / ENDS: Not together = n!
- WHAT — NOT TOGETHER / ENDS: Not together = n! - (together). A particular person at an end: 2 * (n-1)! for a line. Read 'at least
Together uses a block. Not together is usually total minus together, not a new guess.
For long answers on Not Together / Ends: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- complement
- together: glue as one super person
- not together: all - together
- NOT TOGETHER / ENDS: Not together = n! - (together). A particular person at an end: 2 * (n-1)! for a line. Read 'at least
Important formulas
- complement
- together: glue as one super person
- not together: all - together
Common exam traps
- Together uses a block. Not together is usually total minus together, not a new guess.
- 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
Together uses a block. Not together is usually total minus together, not a new guess.
- 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
Together uses a block. Not together is usually total minus together, not a new guess.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
complement
together: glue as one super person
not together: all - together
NOT TOGETHER / ENDS: Not together = n! - (together). A particular person at an end: 2 * (n-1)! for a line. Read 'at least
Not together = n! - (together). A particular person at an end: 2 * (n-1)! for a line. Read 'at least one' as a split of cases if needed.
- Definition
- Not together = n! - (together). A particular person at an end: 2 * (n-1)! for a line. Read 'at least one' as a split of cases if needed.
- Example
- All minus glued
- Critical warning
- Together uses a block. Not together is usually total minus together, not a new guess.
Did you understand this topic?
Your answer is saved with your learning record. It does not mark the topic as mastered.
Ready to test yourself?
You've completed the learning section.
Exam Practice
Define
Q1. Define Not Together / Ends.
Explain
Q2. Explain: MAIN IDEA.
Example
Q3. Give one clear example of Not Together / Ends and say why it fits.
Mistake
Q4. State one common mistake students make about Not Together / Ends.
Exam note
Q5. Write a short exam note on Not Together / Ends: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.