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: \[ P(x)=\frac{1}{\sigma\sqrt{2\pi}}\exp\left(-\frac{1}{2}\left(\frac{x- \left\langle x\right\rangle}{\sigma}\right)^2\right) \]

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.

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.