Question 1068090
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{{{highlight(cross(30c3))}}} = {{{highlight(cross(nc4))}}} find n


30C3 = nC4   find n
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The left side is {{{(30*29*28)/(1*2*3)}}}.


The right side is {{{(n*(n-1)*(n-2)*(n-3))/(1*2*3*4)}}}


The equation is   {{{(30*29*28)/(1*2*3)}}} = {{{(n*(n-1)*(n-2)*(n-3))/(1*2*3*4)}}}   or  (canceling common factors in denominators)

30*29*28 = {{{(n*(n-1)*(n-2)*(n-3))/4}}}    or

30*29*28*4 = n*(n-1)*(n-2)*(n-3),   or

n*(n-1)*(n-2)*(n-3) = 97440.

{{{root(4,97440)}}} = 17.67.

Therefore, there are two versions to check

           n = 19  --->  19*18*17*16 =  93024,    and
           n = 20  --->  20*19*18*17 = 116260.

<U>Answer</U>.  This equation HAS NO solutions in integer numbers.
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