sequences 2

[red and white kop!]

this problem involves Pascal-sequence notation and i'm not sure how to do that, so i will use (n r)

(n r) = n!/(r! x (n-r)!)
assuming this is true, show that (n r)=(n (n-r)).

so basically i have to prove n!/(r! x (n-r)!)=(n (n-r))
i don't know if its useful to develop extensively but i did and it is unclear to me how to combine the two sequences in the denominator of the LHS
all help appreciated

 

[Deleted member 4993]

this problem involves Pascal-sequence notation and i'm not sure how to do that, so i will use (n r)

(n r) = n!/(r! x (n-r)!)
assuming this is true, show that (n r)=(n (n-r)).

so basically i have to prove n!/(r! x (n-r)!)=(n (n-r))
i don't know if its useful to develop extensively but i did and it is unclear to me how to combine the two sequences in the denominator of the LHS
all help appreciated

Come on you are better than that - it is almost one-line proof.....

\(\displaystyle _nC_{n-r} \ = \ \frac{n!}{(n-r)! \cdot [n-(n-r)]!} \ = \ \frac{n!}{(n-r)! \cdot [n-n+r]!} \ = \ \frac{n!}{(n-r)! \cdot r!} \ = \ _nC_{r}\)