I'm trying to understand the practical application of factorial - in simple applications. I searched the math.stackexchange and could not find an answer.
I understand that a factorial of n items gives you the number of ways you can arrange the given items.
For example: If there are two coins - you can arrange them in two different ways - like wise if you have 3 coins - there are 6 ways you can arrange them.
I've the following questions:
- What are the other applications than arranging number of items.
- I'm reading about the gamma function to be used for finding factorials of non-integers (decimals). What is the use of this - as we would never tend to arrange like 2.5 (two-and-a-half) items.
- I plotted the following range of numbers with its factorial using gnuplot (software). I want to know how this software interpolates the value of the factorial between two integers. Because I have not told gnuplot to use the gamma function
number factorial 0 1 1 1 2 2 3 6 4 24 5 120
plot "factorial" using 1:2 smooth bezier
I've very limited knowledge in mathematics - say school level - I'd prefer a simple answer which can be related to easily