Question 947547
<pre>
To prove:

{{{nCr/nC(r-1)}}}{{{""=""}}}{{{(n-r+1)/r}}}

We begin with the left side and we show that
it equals the right side:

{{{nCr/nC(r-1)}}}

{{{nCr}}}{{{"÷"}}}{{{nC(r-1)}}}

{{{n!/(r!(n-r)!)}}}{{{"÷"}}}{{{n!/((r-1)!(n^""-(r-1))! )}}}

{{{n!/(r!(n-r)!)}}}{{{"÷"}}}{{{n!/((r-1)!(n-r+1)! )}}}

{{{n!/(r!(n-r)!)}}}{{{"×"}}}{{{((r-1)!(n-r+1)! )/n!}}}


{{{cross(n!)/(r!(n-r)!)}}}{{{"×"}}}{{{((r-1)!(n-r+1)! )/cross(n!)}}}

{{{(r-1)!(n-r+1)!/(r!*(n-r)!)}}}

Write (n-r+1)! as (n-r+1)(n-r)! and r! as r(r-1)!

{{{((r-1)!(n-r+1)(n-r)!)/(r*(r-1)!*(n-r)!)}}}

{{{(cross((r-1)!)(n-r+1)cross((n-r)!))/(r*cross((r-1)!)*cross((n-r)!))}}}

{{{(n-r+1)/r}}}

Edwin</pre>