Question

If ²ⁿC₃ : ⁿC₂ = 44 : 3, find n.

Answer 1

Given :

²ⁿC₃ : ⁿC₂ = 44 : 3

We know that,

ⁿC_r = \(\frac{n!}{r!(n-r)!}\)

And also,

n! = n(n – 1)(n – 2)…………2.1

⇒ 2 × (2n – 1) × 2 = 44 

⇒ 2n – 1 = 11 

⇒ 2n = 12

⇒ n = \(\frac{12}{2}\) 

⇒ n = 6 

∴ The value of n is 6.