Question 179352
<font size = 5 color = "red"><b>Edwin's solution:
Mathtut's solution is incorrect as he misinterpreted your problem.</font></b>

Find the value of the following: 
{{{(6!10!)/(4!12!)}}} 
If your answer is not an integer, write it as an exact fraction.
<pre><font size = 4 color = "indigo"><b>
{{{((6*5*4*3*2*1)(10*9*8*7*6*5*4*3*2*1))/((4*3*2*1)(12*11*10*9*8*7*6*5*4*3*2*1))}}} 

Now cancel the {{{4*3*2*1}}}'s

{{{((6*5*cross(4*3*2*1))(10*9*8*7*6*5*4*3*2*1))/((cross(4*3*2*1))(12*11*10*9*8*7*6*5*4*3*2*1))}}}

Now cancel the {{{10*9*8*7*6*5*4*3*2*1}}}'s

{{{((6*5*cross(4*3*2*1))(cross(10*9*8*7*6*5*4*3*2*1)))/((cross(4*3*2*1))(12*11*cross(10*9*8*7*6*5*4*3*2*1)))}}}

and you are left with

{{{(6*5)/(12*11)}}}

Now cancel the {{{6}}} into to {{{12}}}, 
getting {{{2}}} on the bottom:

{{{(cross(6)*5)/(cross(12[2])*11)}}}

and you have

{{{5/(2*11)}}}

or

{{{5/22}}}

Edwin</pre>