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