How can i find all of the numbers in a certain row of pascals triangle, for this example lets say the 11th row, without having to draw out the entire triangle?
In: Mathematics
The numbers on pascal’s triangle represent the number of possible paths you could take from the top to that place on the triangle. So it shouldn’t be too surprising that we use the same math to calculate values in pascal’s triangle as we use to calculate combinations (ie all the possible combinations of going left or right to get to a place).
For calculating combinations we use what’s called a choose function. It takes in two values that we’ll call n and k. This can easily be calculated using factorials, where “n choose k” equals n!/(k!*(n-k)!).
You can get all the numbers of a given row on pascals triangle by setting n to the value of the row, and then running through the values of k from 0 to n. (This assumes the top row is 0).
So the values of the 11th row are:
11choose0, 11choose1, 11choose2, …,11choose11
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