Find the equation in the form of 39 n 39 given that nC3 3C1 nC8 5C2 ........

Quantitative Aptitude (CDS) Permutation & Combination

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Find the equation in the form of 'n' ,given that- nC3 + 3C1 =nC8 + 5C2 ?

n^3 -8n^2 +5n -42=0

n^3 -6n^2 +5n -42=0

n^3 -6n^2 +8n -42=0

n^3 -6n^2 +5n -52=0

Explanation:

nC3 + 3C1 =n C2+5C 2
n! /3! n-3! +3! /2! =n! /2!n-2! +5! /2! 3!
n ×n-1×n-2/6 +3 =n(n-1) /2 +10
n ×n-1×n-2/6 =n(n-1) /2 +7
n ×n-1×n-2/6 -n(n-1) /2=7
(n×n-1/2) (n-2/3 -1) =7
(n×n-1/2) (n-5/3) =7
n (n-1) (n-5) =42
n^3 -n^2 -5n^2 +5n=42
n^3 -6n^2 +5n -42=0