The page you are reading is part of a draft (v2.0) of the "No bullshit guide to math and physics."
The text has since gone through many edits and is now available in print and electronic format. The current edition of the book is v4.0, which is a substantial improvement in terms of content and language (I hired a professional editor) from the draft version.
I'm leaving the old wiki content up for the time being, but I highly engourage you to check out the finished book. You can check out an extended preview here (PDF, 106 pages, 5MB).
Combinations
The number of possible {combinations} of $k$ elements from $n$ elements is given by \[ {n\choose k}=\frac{n!}{k!(n-k)!} \] The number of {permutations} of $p$ from $n$ is given by \[ \frac{n!}{(n-p)!}=p!{n\choose p} \] The number of different ways to classify $n_i$ elements in $i$ groups, when the total number of elements is $N$, is \[ \frac{N!}{\prod\limits_i n_i!} \]
{The Normal distribution} is a limiting case of the binomial distribution for continuous variables: \[ P(x)=\frac{1}{\sigma\sqrt{2\pi}}\exp\left(-\frac{1}{2}\left(\frac{x- \left\langle x\right\rangle}{\sigma}\right)^2\right) \]
Examples
Factorial example
5! = 120 since 5*4=20, 5*4*3=60, 5*4*3*2=120, 5*4*3*2*1=120
== Permutations example Permutations: permutations are the number of things(n) taken ® at a time. It is written nPr. For example: nPn is n! 6P6 is 6*5*4*3*2*1 = 720 however… 6P3 is 6*5*4 = 120 It is 6!, but it stops after going around 3 times, not at the number 3. 8P5 = 8*7*6*5*4 = 6,720 Another way of looking at it is 8P5 = 8!/(8-5)! Either way, same answer.
Combinations example
are a way of looking at things without worrying what order they are in. For example, (A+B),(B+A):(A+C),(C+A):(A+D),(D+A and so on; now it looks like {B,A}:{C,A}:{D,A} and so on. The number of Combonations of (n) things taken ® at a time is written nCr–nCr = nPr / r! For example: 4C2 = 4P2 / 2! or (4*3)/(2*1) or 12/2 or 6 7C5 = 7P5 / 5! or (7*6*5*4*3)/(5*4*3*2*1) or 2,520/120 or 21.