Correct Answer - Option 3 : 9
Formula used:
\(^nC_r=\frac{n!}{r!(n-r)!}\)
n! = n × (n - 1) × (n - 2).......3 × 2 × 1
Calculation:
Given that,
4 × nC5 = 9 × n-1C5
Using the above formula
\(4×\frac{n!}{5!(n-5)!}=9×\frac{(n-1)!}{5![(n-1)-5]!}\)
⇒ \(4×\frac{n× (n-1)!}{5!(n-5)(n-6)!}=9×\frac{(n-1)!}{5![(n-6]!}\)
⇒ \(\frac{4n}{(n-5)} = 9\)
⇒ 9n - 45 = 49
⇒ 5n = 45
⇒ n = 9