Question 222506
C(10,4)
<pre><font size = 4 color = "indigo"><b>
The formula is

{{{C(n,r) = n!/(r!(n-r)!)}}}

Substituting:

{{{C(10,4) = 10!/(4!(10-4)!)=10!/(4!6!)=(10*9*8*7*6*5*4*3*2*1)/((4*3*2*1)(6*5*4*3*2*1))}}}

Cancel the {{{6*5*4*3*2*1}}}s:

{{{C(10,4) =(10*9*8*7*cross(6*5*4*3*2*1))/((4*3*2*1)(cross(6*5*4*3*2*1)))}}}

{{{C(10,4) =(10*9*8*7)/(4*3*2*1)}}}

Cancel the {{{4}}} and {{{2}}} in the bottom into 
the {{{8}}} on top

{{{C(10,4) =(10*9*cross(8)*7)/(cross(4)*3*cross(2)*1)}}}

{{{C(10,4) =(10*9*7)/(3*1)}}}

Cancel the 3 in the bottom into the 9 on top leaving 3 on top:

        {{{3}}}
{{{C(10,4) =(10*cross(9)*7)/(cross(3)*1)}}}

{{{C(10,4) =(10*3*7)/(1)}}}

{{{C(10,4)=210}}}

Edwin</pre>