Permutations and Combinations

For the discussion of math. Duh.

Moderators: gmalivuk, Moderators General, Prelates

User avatar
free-bee
Posts: 282
Joined: Tue Nov 20, 2012 1:35 pm UTC
Location: London, KY

Permutations and Combinations

Postby free-bee » Sun Nov 03, 2013 4:05 am UTC

Over at a video game forum, someone asked how many different looks your character can have. I have not done these types of problems in two+ years. The numbers needed are currently unknown. So I will make up a problem from the top of my head which covers the question similarly.

Pretend you run a fan manufacturing business. Your fans can/will vary in terms of physical characteristics. Here are the possible options:
Fan Speed (x1000 RPM): 1, 2, 3
Number of Blades: 2, 3, 4, 5, 6, 7
Color: Pink, Black, Camouflage
Mist Sprayer: Yes/No

How many different fans can be produced?
I assume you count the options for each category and multiply them? If so, then the answer - in this specific question - is 3*6*3*2 = 108?
my sister wrote:[the sun] can go to Hell and brighten that place up a while.

FancyHat
Posts: 341
Joined: Thu Oct 25, 2012 7:28 pm UTC

Re: Permutations and Combinations

Postby FancyHat » Sun Nov 03, 2013 4:09 am UTC

Yes.
I am male, I am 'him'.

User avatar
Flumble
Yes Man
Posts: 2249
Joined: Sun Aug 05, 2012 9:35 pm UTC

Re: Permutations and Combinations

Postby Flumble » Sun Nov 03, 2013 1:57 pm UTC

To add to that: in general, if two choices are independent, you get the total number of possibilities by multiplying those of the individual choices.

User avatar
dudiobugtron
Posts: 1098
Joined: Mon Jul 30, 2012 9:14 am UTC
Location: The Outlier

Re: Permutations and Combinations

Postby dudiobugtron » Mon Nov 04, 2013 1:35 am UTC

Flumble wrote:To add to that: in general, if two choices are independent not mutually exclusive, you get the total number of possibilities by multiplying those of the individual choices.

Pedantically Robustened ;). You don't need independence to get the total number of possibilites.
Image

DavCrav
Posts: 251
Joined: Tue Aug 12, 2008 3:04 pm UTC
Location: Oxford, UK

Re: Permutations and Combinations

Postby DavCrav » Mon Nov 04, 2013 10:42 am UTC

I don't think that's clear. You do need independence of some sort, not just not mutually exclusive.

Here is an example, in the spirit of the OP: we'll take clothing and sex. There are (generically) two options for sex, but depending on the choice of sex, only certain clothing options might be available. You cannot simply multiply the (say) twnety clothing options by two sexes, even though sex and clothing are not mutually exclusive.

(You can decide whether this whole scenario was just a build up for that last line, a la http://xkcd.com/410.)

User avatar
jaap
Posts: 2094
Joined: Fri Jul 06, 2007 7:06 am UTC
Contact:

Re: Permutations and Combinations

Postby jaap » Mon Nov 04, 2013 2:53 pm UTC

DavCrav wrote:I don't think that's clear. You do need independence of some sort, not just not mutually exclusive.

Here is an example, in the spirit of the OP: we'll take clothing and sex. There are (generically) two options for sex, but depending on the choice of sex, only certain clothing options might be available. You cannot simply multiply the (say) twnety clothing options by two sexes, even though sex and clothing are not mutually exclusive.

(You can decide whether this whole scenario was just a build up for that last line, a la http://xkcd.com/410.)

So in your example certain clothes choices are excluded for certain sexes (and vice versa), i.e. those particular choices are mutually exclusive.

The problem with using 'independence' is that choices and combinations are often used in probability theory, and independence in that context is a far stronger requirement than needed if you only want to count all the combinations with non-zero probability (i.e. those that are not mutually exclusive).

DavCrav
Posts: 251
Joined: Tue Aug 12, 2008 3:04 pm UTC
Location: Oxford, UK

Re: Permutations and Combinations

Postby DavCrav » Mon Nov 04, 2013 10:53 pm UTC

Hmm. So independent and mutually exclusive look like the same thing in this case. In which case, it isn't robustened, or whatever somebody earlier said. If they are different things, what is the difference in the context of combinations?

User avatar
dudiobugtron
Posts: 1098
Joined: Mon Jul 30, 2012 9:14 am UTC
Location: The Outlier

Re: Permutations and Combinations

Postby dudiobugtron » Tue Nov 05, 2013 12:22 am UTC

I think by attempting to 'robusten' it, I just made it ambiguous.

Here's an example that might help clear up what I meant.

Imagine you have two pairs of jeans (red and blue), and two tops (red and blue). You have to decide which ones to wear. You like colour-matching, so if you want to wear a blue top, that means you're more likely to also wear blue jeans. So the choices are not independent. However, you still might sometimes choose to wear the blue top with red jeans; if your blue jeans were in the wash, for example. So, they aren't mutually exlclusive.

There are four possible combinations in this setup RR, BB are the two most likely, but also RB and BR are possible.

However, if you never wore the red jeans with the blue top (because you hated that combination), then those two choices are mutually exclusive. So it's no longer one of the possible options.

As you can see, whether or not two choices are independent doesn't affect which combinations are possible, it just affects the chance of choosing those combinations. You only need to worry about whether they are mutually exclusive.
Image


Return to “Mathematics”

Who is online

Users browsing this forum: No registered users and 7 guests