Thread: Pascal's Rule

Hi this question was in Advanced Higher Maths in the UK
Show that (n+1 , 3) - (n ,3 )=(n ,2)
They are written in column vector form ie n+1 at top and 3 at the bottom for example for the first. I think you have to use the n c r formula to prove the rhs
Please Help. A member kindly said it was this rule but I don't know how to prove
it for this question using the identity:

(n , r-1)+(n ,r)=(n+1, r) written as column vectors

Thanks

Originally Posted by minicooper58

Hi this question was in Advanced Higher Maths in the UK
Show that (n+1 , 3) - (n ,3 )=(n ,2)
They are written in column vector form ie n+1 at top and 3 at the bottom for example for the first. I think you have to use the n c r formula to prove the rhs
Please Help. A member kindly said it was this rule but I don't know how to prove
it for this question using the identity:

(n , r-1)+(n ,r)=(n+1, r) written as column vectors

Thanks

I see you are unsatisfied by my responses in this thread. Why not just ask about what you didn't understand?

Combinatorial proof:

Pascal's Rule states:



Proof:


Let be an element of group of elements.
The number of combinations of elements from group of elements, which is not containing the element is give by: , now, the number of combinations which containing element is: .

But, every combination is containing or not containing . Hence, the total number of combinations of from elements is the sum of the above.

Q.E.D