SOLUTION: Use the definition (n) (r) = n!/ r!(n-r)! to prove that (n) = (n ) (r) (n - r) This is from a binomial theorem part of a textbook. The n and r are in t

Algebra ->  Permutations -> SOLUTION: Use the definition (n) (r) = n!/ r!(n-r)! to prove that (n) = (n ) (r) (n - r) This is from a binomial theorem part of a textbook. The n and r are in t      Log On


   



Question 939593: Use the definition
(n)
(r) = n!/ r!(n-r)! to prove that
(n) = (n )
(r) (n - r)
This is from a binomial theorem part of a textbook.
The n and r are in the same bracket with the letter n on top of r.
Also (n and n-r) are in the same bracket too with n-r being under n.
Sorry I wasn't sure how to write this question properly on a pc.
Any help on this would be appreciated.

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
%28matrix%282%2C1%2Cn%2Cr%29%29%22%22=%22%22n%21%2F%28r%21%28n-r%29%21%29

Replace r by (n-r)   

%28matrix%282%2C1%2Cn%2C%28n-r%29%29%29%22%22=%22%22n%21%2F%28%28n-r%29%21%5E%22%22%28n%5E%22%22-%28n-r%29%29%21%29

%28matrix%282%2C1%2Cn%2Cn-r%29%29%22%22=%22%22n%21%2F%28%28n-r%29%21%28n-n%2Br%29%21%29

%28matrix%282%2C1%2Cn%2Cn-r%29%29%22%22=%22%22n%21%2F%28%28n-r%29%21r%21%29%22%22=%22%22n%21%2F%28r%21%28n-r%29%21%29%22%22=%22%22%28matrix%282%2C1%2Cn%2Cr%29%29

Edwin