Factorial Identities
Key Questions
-
A factorial is a number multiplied by all of the integers below it.
Eg, "Four factorial"
=4! =4xx3xx2xx1=24 
Mike G.
·
1
·
Apr 7 2015
-
Answer:
Many things in various areas of mathematics.
Explanation:
Here are a few examples:
Probability (Combinatorics)
If a fair coin is tossed 10 times, what is the probability of exactly
6 heads?Answer:
(10!)/(6! 4! 2^10) Series for sin, cos and exponential functions
sin(x) = x - x^3/(3!) + x^5/(5!) -x^7/(7!)+... cos(x) = 1 - x^2/(2!) + x^4/(4!) - x^6/(6!) +... e^x = 1 + x + x^2/(2!) + x^3/(3!) + x^4/(4!) + ... Taylor Series
f(x) = f(a)/(0!)+(f'(a))/(1!)(x-a)+(f''(a))/(2!)(x-a)^2+(f'''(a))/(3!)(x-a)^3+... Binomial Expansion
(a+b)^n = ((n),(0))a^n + ((n),(1))a^(n-1)b + ((n),(2))a^(n-2)b^2 +...+((n),(n))b^n where
((n),(k)) = (n!)/(k!(n-k)!) 
George C.
·
2
·
Sep 6 2015
-
The factorial of a number n is denoted as
n! This is the product of all numbers from 1 to n.
So we have
n! = n * (n - 1) * (n -2) * … * 2 * 1 So let us take
6! 6! = 6 * 5 * 4 * 3 * 2 * 1 6! = 720 
Don S.
·
·
Oct 1 2014