If n C 8 = n C 2 , find n C 2.

Question

Philoid · Accepted Answer

Given: ⁿC₈ = ⁿC₂

We know that if ⁿC_r = ⁿC_p then either r = p or r = n – p

Here ⁿC₈ = ⁿC₂

⇒ 8 = n – 2

⇒ n = 10

Now,

∴ ⁿC₂= ¹⁰C₂ = (∵ ⁿC_r = )

⇒¹⁰C₂ =

If nC8 = nC2, find nC2.