SOLUTION: For any integer n ≥ 3. Find n if C(n,3) + P(n,2) = 952. Please show your work.

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Question 1063319: For any integer n ≥ 3. Find n if C(n,3) + P(n,2) = 952. Please show your work.
Answer by ikleyn(52832) About Me  (Show Source):
You can put this solution on YOUR website!
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highlight%28cross%28For%29%29 highlight%28cross%28any%29%29 Find integer n ≥ 3, such that highlight%28cross%28n_if%29%29 C(n,3) + P(n,2) = 952. Please show your work.
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%28n%2A%28n-1%29%2A%28n-2%29%29%2F6+%2B+n%2A%28n-1%29 = 952,   --->

n%2A%28n-1%29%2A%28%28n-2%29%2F6+%2B+1%29 = 952,

n*(n-1)*(n+4) = 6*952,

n*(n-1)*(n+4) = 5712.      ( Now, root%283%2C6712%29 = 17.8...,  therefore, try n = 17 )

17*16*21 = 5712.

Answer. n = 17.