Turn on thread page Beta

need help 4 emma's dilemma math coursework justification and proof of formula watch

    • Thread Starter

    can any1 help me with the justification of the emmas dilemma formula?

    the formula is:

    ---- = number of arrangerments
    A!B!C! etc.

    A/B/C being the the number of repeats
    X being number of letters

    3!2! (due to 3 a's and 2 b's)

    can any1 help me justify and prove this?

    well look at it this way:

    You have X letters to pick
    You pick them one by one, and lay them out in the order you pick them
    For the first letter there are X possiblities
    For the second letter there are X-1 possiblities
    and so on, until you have X! different ways of arranging the letters

    BUT THEN you notice that some of those are the same - they arent all unique ways of ordering them. Lets say that two of the letters available to choose were the same. That means that for every arrangement of letters, there would be one other identical arrangement - because you could just swap the two matching letters.
    OK so what if there was 3 of the same letters. Well then you will have every unique arrangement repeating 6 times, since there are six different ways of order the 3 repeated letters.
    So you do X! then divide it by A! where A is the number of duplicated letters

    Then the result you get, you can imagine checking it again, and seeing if you have any duplications in the arrangements. If you had another few identical letters available then once again you would have duplications, the number of duplications of each arrangement equaling the number of ways of arranging those letters - so you divide again by B!, and so on
    • Thread Starter

    that clears things up
    thx for help!
    • Thread Starter

    does ne1 no the format for writing a math coursework?
Turn on thread page Beta
Updated: June 23, 2004

University open days

  1. Loughborough University
    General Open Day Undergraduate
    Fri, 21 Sep '18
  2. University of Cambridge
    Churchill College Undergraduate
    Fri, 21 Sep '18
  3. Richmond, The American International University in London
    Undergraduate Open Day Undergraduate
    Fri, 21 Sep '18
Which accompaniment is best?
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.