Question

Solve for n: C(n+1,4)=6C(n-1,2)

Answer 1

Answer:

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Step-by-step explanation:

(n+1)! / [ 4!⋅((n+1)−4)! ] = 6⋅(n−1)! / [ 2!⋅((n−1)−2)! ]

(n+1)! / [ 4!⋅(n−3)! ] = 6⋅(n−1)! / [ 2!⋅(n−3)! ]

(n+1)! / (4!) = 6⋅(n−1)! / (2!)

(n+1)! / 24 = 6⋅(n−1)! / 2

(n+1)! = 72⋅(n−1)!

(n+1)⋅n⋅(n−1)! = 72⋅(n−1)!

(n+1)⋅n = 72

n² + n = 72

n² + n − 72 = 0

(n+9)(n−8) = 0

n = −9 or 8

But n cannot be negative

So n=8