Results are out! Find what you need...fast. Get quick advice or join the chat
x

Unlock these great extras with your FREE membership

  • One-on-one advice about results day and Clearing
  • Free access to our personal statement wizard
  • Customise TSR to suit how you want to use it

Multinomial/combinatorics question

Announcements Posted on
Rate your uni — help us build a league table based on real student views 19-08-2015
  1. Offline

    ReputationRep:
    Question: Consider the word COMBINATORICS. What is the probability on the arrangements containing the word COMIC without interruption?

    I think.....we have 2 options for C (appearing at front or back), 2 options for O and 2 options for I. The word COMIC can then be placed in 13-5+1 = 9 places, and the remaining words can be arranged in 8! ways. So this gives 2 x 2 x 2 x 9 x 8!

    We then divide this by (13!/3.*2!), which is the total number of combinations.

    But then the next question is:

    How many different ways can the word COMIC be made from the letters of COMBINATORICS if the position the letters came from in COMBINATORICS distinguishes alike letters?

    So I'm confused...should my answer to this part be my answer to the previous part, and for the previous part should the number of ways be just 9 * 8!

    Thanks for any help, really stressing out
  2. Offline

    ReputationRep:
    Does anyone have any advice on this ?
  3. Offline

    ReputationRep:
    (Original post by combinatorix)
    Question: Consider the word COMBINATORICS. What is the probability on the arrangements containing the word COMIC without interruption?

    I think.....we have 2 options for C (appearing at front or back), 2 options for O and 2 options for I.
    I think you have 1 option for C, beacuse you have to select 2 C letters from 2, to form COMIC and you can not distinguish them (which one is at the start and which is at the end position).
    So you have 1 option for O and I, too because you can not distinguish them.
    So you have 8 different letter, it means 8! options, and the COMIC can be placed in 9 places so 9*8!=9!
    The word COMIC can then be placed in 13-5+1 = 9 places, and the remaining words can be arranged in 8! ways. So this gives 2 x 2 x 2 x 9 x 8!

    We then divide this by (13!/3.*2!), which is the total number of combinations.
    We divide by 13!/(2!*2!*2!)

    But then the next question is:

    How many different ways can the word COMIC be made from the letters of COMBINATORICS if the position the letters came from in COMBINATORICS distinguishes alike letters?

    So I'm confused...should my answer to this part be my answer to the previous part, and for the previous part should the number of ways be just 9 * 8!

    Thanks for any help, really stressing out
    Here the answer is that you worked out for Q1

Reply

Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. By joining you agree to our Ts and Cs, privacy policy and site rules

  2. Slide to join now Processing…

Updated: May 11, 2012
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

New on TSR

Rate your uni

Help build a new league table

Poll
How do you read?
Study resources
Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.