5 thoughts on “Pascal’s Triangle and Combinations”

Do we need to make this complete triangle to have the values of nth row. Or is there any short cut to write nth row directly.
Though there exist a pattern through which I can obtain nth row directly but it will take same time as to draw whole triangle.

Well, Dushyant, 2 things on this – firstly, I agree that making the triangle takes as much time as, or a bit more then, calculating a typical nCr value from scratch (say 8C3). So if you want only 1 value it doesn’t help if you plan to draw from scratch. But if we rapidly need 4-5 nCr values, as often happens, then it takes the same time, pretty much, to get 4-5 values by this method as to get one.

Secondly, once you draw out the triangle a few times in practice, the first few rows will pretty much get memorised and you can start from there…for example I know up till the 7th or 8th row by heart having used it often – so now I can just start by doing 1 7 21 35 35 21 7 1 and generate further as required ðŸ™‚

Do we need to make this complete triangle to have the values of nth row. Or is there any short cut to write nth row directly.

Though there exist a pattern through which I can obtain nth row directly but it will take same time as to draw whole triangle.

Well, Dushyant, 2 things on this – firstly, I agree that making the triangle takes as much time as, or a bit more then, calculating a typical nCr value from scratch (say 8C3). So if you want only 1 value it doesn’t help if you plan to draw from scratch. But if we rapidly need 4-5 nCr values, as often happens, then it takes the same time, pretty much, to get 4-5 values by this method as to get one.

Secondly, once you draw out the triangle a few times in practice, the first few rows will pretty much get memorised and you can start from there…for example I know up till the 7th or 8th row by heart having used it often – so now I can just start by doing 1 7 21 35 35 21 7 1 and generate further as required ðŸ™‚

J

Yes I got the point ðŸ™‚

thank you (y)

Hi Sir,

Could you explain the concept behind expansion of algebraic terms such as number of terms in

(1+x+x^3)^100

Gaurav, you could try this: https://crackthecat.wordpress.com/2013/06/05/the-multinomial-theorem/

regards

J