SOLUTION: 30c3=nc4 find n

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Question 1068090: 30c3=nc4 find n
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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highlight%28cross%2830c3%29%29 = highlight%28cross%28nc4%29%29 find n

30C3 = nC4 find n
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The left side is %2830%2A29%2A28%29%2F%281%2A2%2A3%29.


The right side is %28n%2A%28n-1%29%2A%28n-2%29%2A%28n-3%29%29%2F%281%2A2%2A3%2A4%29


The equation is   %2830%2A29%2A28%29%2F%281%2A2%2A3%29 = %28n%2A%28n-1%29%2A%28n-2%29%2A%28n-3%29%29%2F%281%2A2%2A3%2A4%29   or  (canceling common factors in denominators)

30*29*28 = %28n%2A%28n-1%29%2A%28n-2%29%2A%28n-3%29%29%2F4    or

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

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

root%284%2C97440%29 = 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.