Can someone show me the relation of the Pascal triangle and combinations?
The Pascal triangle is a formation of numbers which is arrived at in the following way:
We start with the topmost row called row zero with a single term whose value is 1.
The row below it has two terms
The row below that has 3 terms and so on with the number of terms increasing by 1 for each new row that is added
Now you add the numbers on the terms resting above any term to arrive at the value of that term. In case only one term rests on a term the other is taken to be 0.
So the first row has .............. 1
The second row has............. 1 1
The third row has.............. 1 2 1
The fourth row has........ 1 3 3 1
Now, from the Pascal triangle one can find the value of C (n, r). Here n is taken to number of the row and r is the number of the column. For example C (3, 2) = 3! / 2!*1! = 3. Looking at the triangle the term to be considered also has the value 3.
You will also find the Pascal triangle to be symmetrical. It can be built larger by adding as many rows as you want, though that will take some time.