Can you list four or so binomial factorials?

Question

adamaero · Answer

Do they have something to do with Pascal's triangle? I found a few so far: n! n factorial, n(n-1)(n-2)...(3)(2)(1) http://www.chilimath.com/algebra/intermediate/fac/factorials-with-variables.html http://www.priklady.eu/en/Mathematics/Combinatorics/Factorial-Binomial-Coefficient.alej Don't understand this though: http://upload.wikimedia.org/math/2/c/0/2c051898c00add06862a5d6a4f975408.png

geerky42 · Answer

http://www.mathsisfun.com/pascals-triangle.html http://www.mathsisfun.com/algebra/binomial-theorem.html

math&ing001 · Answer

Yes binomial coefficient can be found with Pascal's triangle or using the formula $C_n^k=\frac{ n! }{ k!(n-k)! }$ 
The third link you posted is simply the binomial formula $$(a+b)^{n}=\sum_{k=0}^{n}C _{n}^{k} a ^{n-k} b ^{k}$$

geerky42 · Answer

attachment

mathmath333 · Answer

$\large\tt \begin{align} \color{black}{(a+b)^2=\color{red}{1}a^2+\color{red}{2}ab+\color{red}{1}b^2}\
\\~~~~~~~~~(a+b)^3=\color{red}{1}a^3+\color{red}{3}a^2b++\color{red}{3}ab^2+\color{red}{1}b^3...\end{align}$

adamaero · Answer

I should've stopped everyone earlier, but I did mean factorials: n!--not factors.

adamaero · Answer

(I didn't look close enough at the binomial formula to realize just what it was)