Question

Find \( n \), if \( { }^{n} C _{8}={ }^{n} C _{6} \).

Answer 1

n!​​​​​​/(n-8)!8!=n!/(n-6)!6!

(n-6)(n-7)=8×7

n=14

Answer 2

Given ⁿC₈ = ⁿC₆

⇒ \(\frac {n!}{8!(n - 8)!} = \frac{n!}{6!(n - 6)!}\)

⇒ \(\frac 1{8.7} = \frac 1{(n - 6)(n - 7)}\)

⇒ (n − 6) (n − 7) = 56

⇒ n² − 13n − 14 = 0

⇒ n = −1 or 14

n cannot be negative so n ≠ -1.

So, n = 14.

Hence, the value of n is​ 14.