Answer:
n = 10
Explanation:
From the question,
nC6 = nC4
n!/6!(n-6)! = n!/4!(n-4)!
Simplifying n! out of the equation
⇒ 1/6!(n-6)! = 1/4!(n-4)!
Crossmultiplying
4!(n-4)! = 6!(n-6)!
4!(n-4)! = 6×5×4!(n-6)!
(n-4)! = 30(n-6)!
(n-4)(n-5)(n-6)! = 30(n-6)!
⇒ (n-4)(n-5) = 30
n²-4n-5n+20 = 30
n²-9n+20-30
n²-9n-10 = 0
Solving the quadratic equation,
n-10n+n-10 = 0
(n-10n)+(n-10) = 0
n(n-10)+1(n-10) = 0
(n+1)(n-10) = 0
Either
n+1 = 0
n = -1
or
n-10 = 0
n = 10
n canot be a negative value,
Therefore, n = 10