SOLUTION: Use the fact that nCr = n!/(n-r)!r! to show that: a.). nCr = nCn-r b.) (n/r)(n-1Cr-1) = nCr

Algebra ->  Permutations -> SOLUTION: Use the fact that nCr = n!/(n-r)!r! to show that: a.). nCr = nCn-r b.) (n/r)(n-1Cr-1) = nCr      Log On


   

Question 947488: Use the fact that nCr = n!/(n-r)!r! to show that:
a.). nCr = nCn-r
b.) (n/r)(n-1Cr-1) = nCr
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
nC%28n-r%29%22%22=%22%22n%21%2F%28+%28n-r%29%29%21%28n-%28n-r%29%5E%22%22%29%21%29%22%22=%22%22n%21%2F+%28%28n-r%29%21%28n-n%2Br%29%21%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%22nCr

------------------------------------------------

 %28n%2Fr%29%28%28n-1%29%5E%22%22C%28r-1%29%29%22%22=%22%22%28n%2Fr%29expr%28%28n-1%29%21%2F%28%28r-1%29%21%28%28n-1%29-%28r-1%29%29%29%29%22%22=%22%22%28n%2Fr%29expr%28%28n-1%29%21%2F%28%28r-1%29%21%28n-1-r%2B1%29%29%29%22%22=%22%22

%28n%2Fr%29expr%28%28n-1%29%21%2F%28%28r-1%29%21%28n-r%29%21%29%29%22%22=%22%22expr%28%28n%2A%28n-1%29%21%29%2F%28r%2A%28r-1%29%21%28n-r%29%21%29%29%22%22=%22%22

     [since n%2A%28n-1%29%21=n%21 and r%2A%28r-1%29%21=r%21]

expr%28n%21%2F%28r%21%2A%28n-r%29%21%29%29%22%22=%22%22nCr

Edwin