Question 1192505
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The expression "(11,r)!" has no meaning.  I will assume you mean "(11-r)!".<br>
{{{C(18,17)=C(18,1)=18}}}<br>
{{{11!/(r!(11-r)!)=C(11,r)}}}<br>
Your equation is<br>
{{{11!/(r!(11-r)!)-6=18}}}
{{{11!/(r!(11-r)!)=C(11,r)=24}}}<br>
The values of C(11,r) are 1, 11, 55, ....<br>
There is no r for which C(11,r) = 24.<br>
The problem as you show it is faulty.<br>