Pascal’s Triangle and Combinations

5 thoughts on “Pascal’s Triangle and Combinations”

1. dushyant133 |

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

• dushyant133 |

Yes I got the point ðŸ™‚
thank you (y)

2. gaurav raj |

Hi Sir,

Could you explain the concept behind expansion of algebraic terms such as number of terms in
(1+x+x^3)^100