SOLUTION: Write the following expression without using the factorial symbol. nC3 + nC2 + nC1 The formula given is n!/r!(n-r)!. My teacher was saying the answer is n^3 + 5n/6. Im ver

Question 1002016: Write the following expression without using the factorial symbol.
nC3 + nC2 + nC1
The formula given is n!/r!(n-r)!.
My teacher was saying the answer is n^3 + 5n/6.
Im very curious as to how the question is written in each step. I have tried many times to get an answer similiar to this. Thank you so much in advance!!
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
n!/(n-3)!3!=n(n-1)(n-2)/6; n(n-1)(n-2)=(n^2-n)(n-2)=(n^3-3n^2+2n)/6
n!/(n-2)!2!=n(n-1)/2
n
n+(n^2-n)/2+(n^3-3n^2+2n)/6=
multiply everything by (6/6)=1
(6n+3n^2-3n+n^3-3n^2+2n)/6
(n^3+5n)/6
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