SOLUTION: 30c3=nc4 find n

Question 1068090: 30c3=nc4 find n

Answer by ikleyn(52804) (Show Source): You can put this solution on YOUR website!
.
= find n

30C3 = nC4 find n
~~~~~~~~~~~~~~~~~~~

The left side is .


The right side is 


The equation is    =    or  (canceling common factors in denominators)

30*29*28 =     or

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

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

Answer.  This equation HAS NO solutions in integer numbers.

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