Anyone here good at Perms & Combs? (1 Viewer)

[Starcraftmazter]

Another question....well 4 little ones, probably the last for some while, since this test is tomorrow.

I've never been good at permutations and combinations, when we were actually studing the topic, I understood it most of the time, and got things right maybe 70% of the time, but now....well. I re-read all the stuff I had, but yet I still get these things wrong.

I did the following 4 questions, and got all of them wrong on my first try. I re-did 3 question, the other.


The questions themselves are small, but the process to get the right answer to me is undefined.

Q4. There are nine people from which any seven may be seated around a circular table. How many arrangements are possible?

Q6. In how many ways may a mixed doubled tennis match be arranged from six married couples if no husband and wife are to play in the same match?

Q10.
i) In how many ways may the letters of the word TOMORROW be arranged?

ii) How many of these arrangements begin with the letter O?

iii) In how many of these arrangements are the three O's rogether?

Q17. Let S = {a, b, c, d, e, f, g, h, i, j} be the set consisting of the first ten letters of the alphabet.

(a) How many subsets of S contain at least three letters?

(b) How many subsets with at least three letters do not contain any vowels?

(c) How many subsets with at least three do not contain any vowels but do contain the letter 'b'?


So here is my re-working of questions 4, 10, 17.
Am I right? Or wrong.....

And question 6, my first attempt was to get the total arrangements, I think 10C4, and subtract the number of arrangements with husband & wife together, but I didn't get it right, I think I might have gotten the latter part of that wrong. Now i just don't know how to do it.


Thanks a lot :rofl:

 

[Starcraftmazter]

Thanks for your help Webby.

In relation to question 6, yes it does appear as though it's just how many ways there are of arranging a single match, out of the given couples.

I've read carefuly, and am certain I understand your logic in all of the questions.

I'm just looking more carefully at 6, I think you misunderstood one part of the question, the one where no husband in wife are to play in the same match - not just on the same team.