Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter

    Find the number of permutations of the letters of the word TOPOLOGY. In how many of these permutations are no two Os together?
    • Thread Starter

    How many different signals can be made from one green, three identical red and two identical blue flags if at least five of them are used?

    We are not here to do your work for you. I have given you a hint for one question so please take time to think over it.
    • Community Assistant

    Community Assistant
    If I asked how many ways can you organise the letters abc you would say 3! So this is like that except now some letters are repeated so we are going to end up with some identical words if we do it this way. So we need to do some division to get rid of the identical ones.

    Complete this:
    1 T
    3 O
    ? P
    ? L
    ? G
    ? Y

    So if we did it like the abc example, how many words would we have?
    But, for example, we have 3Os so there are 3! ways we can organise the Os, so we need to divide by something...
    Do the same for the other letters with repetition.

    For no two Os together, treat OO as one letter. So now you have:
    1 T
    2 O
    So work out how many words there can be like this.
    But this is working out how many have OO together, so you need to subtract this number from something to get the answer.

    I hope this helps somehow. It's hard to explain it without just giving the calculations. :-/

    Posted from TSR Mobile
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Would you rather give up salt or pepper?
    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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.