Combinatorics.Exclude when specific thing is before another.

For the discussion of math. Duh.

Moderators: gmalivuk, Moderators General, Prelates

User avatar
jacksmack
Posts: 83
Joined: Wed Mar 21, 2012 2:18 am UTC
Location: Italy

Combinatorics.Exclude when specific thing is before another.

Postby jacksmack » Fri Feb 27, 2015 12:05 pm UTC

Hi,

I have some problems with this exercise about combinatorics. Please can you help me to resolve that? :

Five guys: John, Jack, Greg, Matt, Eric, will be speaking at a meeting. How many ways can they take their turn without Jack speaking before John?
[Answer: 60]

I have done my own reasoning, as follows:
I have considered the case without restrictions: 5! = 120 ways.
And then I considered John and Jack as unique group I can arrange in 4! = 24 ways. I haven't considered the arrangement 2! for that group because I consider only the case where Jack is before John and not vice versa.
But when I do the calculation: 120 - 24 = 96

that it is different from the answer given in the textbook. Where is the error? Maybe Do I have to interpretate the exercise in a different way?

many thanks!

User avatar
elliptic
Posts: 34
Joined: Tue Aug 14, 2012 2:21 pm UTC
Location: UK

Re: Combinatorics.Exclude when specific thing is before anot

Postby elliptic » Fri Feb 27, 2015 12:19 pm UTC

Total number of speaker orderings N(total) = 5! = 120.

By symmetry, N(Jack before John) = N(John before Jack).

Therefore, N(John before Jack) = N(total) / 2 = 60.

User avatar
Sizik
Posts: 1260
Joined: Wed Aug 27, 2008 3:48 am UTC

Re: Combinatorics.Exclude when specific thing is before anot

Postby Sizik » Fri Feb 27, 2015 1:44 pm UTC

jacksmack wrote:I have done my own reasoning, as follows:
I have considered the case without restrictions: 5! = 120 ways.
And then I considered John and Jack as unique group I can arrange in 4! = 24 ways. I haven't considered the arrangement 2! for that group because I consider only the case where Jack is before John and not vice versa.
But when I do the calculation: 120 - 24 = 96


By considering Jack and John as one "person" in the lineup, you're only counting the cases where they're sitting right next to each other. Thus, 24 is the number of arrangements where Jack is immediately before John, and doesn't include when Jack is two, three, or four slots ahead.
she/they
gmalivuk wrote:
King Author wrote:If space (rather, distance) is an illusion, it'd be possible for one meta-me to experience both body's sensory inputs.
Yes. And if wishes were horses, wishing wells would fill up very quickly with drowned horses.


Return to “Mathematics”

Who is online

Users browsing this forum: No registered users and 10 guests