You are Here: Home

Multinomial/combinatorics question

Announcements Posted on
Take our survey to be in with the chance of winning a £50 Amazon voucher or one of 5 x £10 Amazon vouchers 28-05-2016
1. 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. Does anyone have any advice on this ?
3. (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

Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
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
1. Oops, you need to agree to our Ts&Cs to register

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.

This forum is supported by:
Today on TSR

Don't be a half-term hermit

How to revise this week and still have a life

Poll
Useful resources

Maths Forum posting guidelines

Not sure where to post? Read here first

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams