how is combinations related to pascals triangle?

Question

 Im having trouble understanding the relationship between these two, and i've looked everywhere but I still don't get it.

Answer 1

Hi Kim, goggle "Pascal's triangle combinations" and you will find some good websites. Pascal's triangle will give you the results for a given combination.

 

Example:

 

If I have 4 things and I want to take 3 at a time, it would be written as "4 take 3." This is represented as:

 

4!/(3! * (4 - 3)!), which has a value of 4.

 

Using Pascal's triangle, and count down to the forth row (remember the first row is the 0 row) and then count from the left 3 places (again remember, the first position is the 0 position) you will find the number 4.

 

          1                          row 0

 

        1  1                        row 1

 

      1  2  1                      row 2

 

    1  3   3   1                  row 3

 

  1  4   6   4   1               row 4, row we look at, from the left, start counting at 0 and continue until you get to 3.

------------------------------------ That will be the number you want.

1  5  10  10   5   1          row 5

 

Try to find the number for "5 take 3" things. The answer is 10. Look at row 5, start counting from the left at 0 until you get to 3 and you will find the number 10 (actually the second 10.)

 

Questions?