SOLUTION: 25. solve for n if P(n,3)=2C(n,2),n € N

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Question 144803:
25. solve for n if P(n,3)=2C(n,2),n € N
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
25. solve for n if P%28n%2C3%29=2C%28n%2C2%29, n € N

P%28N%2CR%29+=+N%2A%28N-1%29%2A%28n-2%29··· (until there are R factors)





So

P%28n%2C3%29=n%28n-1%29%28n-2%29

and

C%28n%2C2%29=n%28n-1%29%2F%282%2A1%29

So

P%28n%2C3%29=2C%28n%2C2%29 

becomes:

n%28n-1%29%28n-2%29=2%28n%28n-1%29%2F2%29

n%28n-1%29%28n-2%29=cross%282%29%28n%28n-1%29%2Fcross%282%29%29

n%28n-1%29%28n-2%29=n%28n-1%29

n%28n-1%29%28n-2%29-n%28n-1%29=0

Factor out n%28n-1%29 on left side:

n%28n-1%29%28%28n-2%29-1%29=0

n%28n-1%29%28n-2-1%29=0

n%28n-1%29%28n-3%29=0

Set each factor = 0

n=0

n-1=0 or n=1

n-3=0 or n=3

So there are three solutions, n=0, n=1, n=3

Edwin