If ⁿC₈ = ⁿC₂, find ⁿC₂

Solution:

Given that, ⁿC₈= ⁿC₂ 

By one of the formulas of combinations, if ⁿCᵣ= ⁿCₚ , then either r = p or r = n - p 

ⁿC₈= ⁿC₂

⇒ 8 = n - 2

n = 10.

Now, 

ⁿC₂ = ¹⁰C₂

= 10! / [2!(10-2)!]  (Using nCr formula)

= 10! / [2!8!]

= 45

NCERT Solutions Class 11 Maths Chapter 7 Exercise 7.4 Question 1

If ⁿC₈ = ⁿC₂, find ⁿC₂

Summary:

If ⁿC₈ = ⁿC₂, then ⁿC₂ = ¹⁰C₂ = 45.