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nP4=84nC2 Solve for n using factorial notation
I'm really struggling with this question and would be grateful for help, please and thank you.
This is what I've tried but it feels really messy and wrong.
n(n-1)(n-2)(n-3)(n-4)!/(n-4)! = 84 {n(n-1)(n-2)!/2!(n-2)!} - This line is wrong. Take it off.
n(n-1)(n-2)(n-3) = 84 {n(n-1)/2} - This line is correct. Keep it.
2{n(n-1)(n-2)(n-3)} = 84{n(n-1)/2) x2/1} - This line is wrong. Take it off.
2{n(n-1)(n-2)(n-3)}/n(n-1) = 84{n(n-1)}/n(n-1) - This line is wrong. Take it off.
2{(n-2)(n-3)}/2 = 84/2 - This line is correct. Keep it.
(n-2)(n-3) = 42 - This line is correct. Keep it.
n^2-5n-36=0 - This line is correct. Keep it.
(n-9)(n+4)=0 - This line is correct. Keep it.
n=9 because n cannot be negative (-4) - This line is correct. Keep it.
Now I really take off the incorrect lines and keep only the correct ones.
nP4=84nC2 Solve for n using factorial notation
n(n-1)(n-2)(n-3) = 84 {n(n-1)/2}
2{n(n-1)(n-2)(n-3)}/(n(n-1)) = 84{n(n-1)}/(n(n-1))
2{(n-2)(n-3)}/2 = 84/2
(n-2)(n-3) = 42
n^2-5n-36=0
(n-9)(n+4)=0
n=9 because n cannot be negative (-4)
Now you have the correct solution.
