I think it would be useful for you to also note that this binomial function also follows Pascal's Triangle:
As you may notice, you begin with the 3 1's at the tip, and to get a number the row below, you simply add the two above that number; eg: 2=1+1, 4=1+3, 10=4+6 as these are above them. The top row is the 0th row, and the left-most number is the 0th one.
Here's the example:
When you say something like
(24) You are looking at the 4th row's 2nd number from the left. As you can see, the binomial function has symmetry which is useful.
I think this can prove useful to some people who may wish to memorise the first few rows of the binomial function.
Edit: This also shows you that within
(rn),
r takes any positive integer values from 0 up to
n and nothing above or below that restriction. This can be notated by
0≤r≤n for
r,n∈N.
You can refer to the actual function to see what if
r>n, then you would be having a factorial of a negative number on the denominator which can't be done as they are undefined due to division by 0; which you should notice if you know the pattern amongst the factorials.