Help with permutations problem

Hi. Not homework. Prompted by situation covered in another thread.

How can this be stated and solved, either simply, or, in what would be another situation when the following set-ups are actually analyzed projectively with percentages/“chance” taken from epidemiological data (not provided here).

Set up:
Guy’s got VD. Had sex with woman.

Exclude genital intercourse. Exclude anal intromission of penis into partner. Infection can be transmitted by oral or anal contact. Either partner can be asymptomatic. What permutations of sexual acts and state of VD of the girl (symptomatic or not) can be adduced? I presume the three, generally speaking, are BJ, cunnilingus, and analingus.

Hell, throw in 69. Just thought of it.

There’s also a very small chance that the rubber broke. In a separate chart/explanation for a layman in this since he forgot high-school math, could you factor that in?

And, finally, I still don’t get the difference between permutation and combination.
Thanks. I can’t wait to tease him geekily. (Like "wife it wealthily.)

Is this a math question, as the title states, or an epidemiology question, as the body seems to be talking about?

I have no idea about the first part. You are not asking about permutations, unless you are asking about how many different ways are there for one of *these *parts to touch one of those parts.

A permutation is the different ways to order a set of elements, like the combination to a lock. Order matters for a permutation.

A combination is the different ways to select a subset of elements, regardless of what order they are in, like rolling dice. In a combination the order is not taken into account.

I think what Leo Bloom is asking is a probability question. To wit: suppose that each particular sex act has a given probability of transmitting some particular disease from a male partner to a female partner. If the couple in question perform acts A, B, and C, what is the likelihood that the female partner will be infected?

If that’s what you’re asking: the naïve way to solve this problem would be to denote the probability of transmission via each act (A, B, C…) as p[sub]A[/sub], p[sub]B[/sub], p[sub]C[/sub], … The probability of not getting infected via each of these acts independently would then be (1 - p[sub]A[/sub]), (1 - p[sub]B[/sub]), (1 - p[sub]C[/sub]), … And, assuming that each of these probabilities are independent of each other, the probability of getting infected via none of these methods is just the product of all of these: 1 - p[sub]A[/sub])(1 - p[sub]B[/sub])(1 - p[sub]C[/sub]) … Finally, the probability of getting infected via at least one of these methods is 1 minus this last number (since the probability of an event happening is 1 minus the probability of it not happening.)

The problem with this method is the statement I bolded above. It’s almost certainly not the case that each of these probabilities are independent of one another, particularly when you’re talking about sex acts performed with one particular partner. In the case of HIV, for instance, “viral load” can vary a lot between partners, and someone with a low viral load is generally less likely to transmit the disease (by any means) than someone with a higher viral load. In other words, if you “luck out” and don’t get the disease via one act, it’s probably the case that you’re less likely to get the disease via another act with the same person.

Permutations and Combinations are taught in basic high school statistics courses and they are one of the few things that are useful to know by most everyone (unlike other subjects). There are many high school textbooks that explain them and teach you all about using them. You can use Google to find many articles about them. My question is why you needed to use such highly charged sexual examples when it would be so simple to instead use Google to find the answers you seek?

MikeS posted a very nice explanation. But if that is not to your liking, I’d suggest you use Google to find a different explanation.

Yes, it is the mathematical statement of certain events. Please excuse the vulgarity. I needed clear verbs; I tried to use symbols, but the graphical logic as I manipulated them became unclear, and I’m sure mathematicians have correct ones which they will use here.

FTR, and for my friends here in SD and posters unknown: As in many of my previous posts, most recently regarding escalator physics, an old/new scientific/mathematical subject has surfaced as interesting in my mind following a quotidian experience. Here, the permutations of actions, for one thing. The additional issue I would welcome being taught by being shown here, however briefly, is something which I believe I should understand when I read certain medical documents: linking the permutations to the likelihood of fuzzy data (as far the individual is concerned), where those links are best put for me to understand the odds of having a particular disease (or whatever) given certain discrete non-fuzzy data.

It sounds jokey, but I am serious as to trying to a) re-understand the elementary math, b) to see how to think about more complicated (for me) cases, again, as pleasure in math, and c) here, as opposed to the escalators, to become a little more numerate when reading/pondering statistical evidence in occasional experiences in real life. Eg, when my wife had some (eventually shown to be-) minor heart problems, I was in wretched hell with epidemiology and mortality statistics. But again, linking statistical data seems to me the second type of question in my OP.

I:
Gonorrhea and chlamydia, each, can present as genital, anal, or pharyngeal. Let us assume only one at a time.
He has genital gonorrhea or genital chlamydia, transmitted by a recent evening with a woman.
Each mode disease can be transmitted by any of those three areas.
She may or may not be symptomatic.

Doctor said “oral sex.” Non genital interaction-to-genital. Exclude anal intromission of penis.

  1. She blew him
  2. He went down on her
  3. She rimmed him
  4. He rimmed her.

II:
They had genital-to-genital sex, including anal, with a condom.
The condom may have broken.

III:
Both set-up I and II above.

IV:
Perhaps there are stats on the likelihood of rates of transmission and condom breakage.

It is indeed difficult to try to use mathematical symbols with this editor. I apologize if I offended you by implying you were being vulgar. No offense was intended.

I don’t know what “escalator physics” means and so I had to use Google to look it up. But most every entry I found referred to the physics of escalators.

Did you intend something else? It would be very interesting if that term meant something other than “the physics of escalators”. I’d really like to know what that could be. But please don’t waste a lot of your time explaining it if it does indeed mean something else. I would be happy with just a link to a page that refers to it.