If α = mC2, then find the value of αC2.

⇒ α = mC2We know that And also n! = n(n – 1)(n – 2)…………2.1⇒ ⇒ ..... (1)We need to find αC2⇒ ⇒ From (1)⇒ ⇒ ⇒ ⇒ ⇒ ∴ The value of αC2 is .

Q15 of 118 Page 18

If α = ^mC₂, then find the value of ^αC₂.

⇒ α = ^mC₂

We know that

And also n! = n(n – 1)(n – 2)…………2.1

⇒

⇒ ..... (1)

We need to find ^αC₂

⇒

From (1)

⇒

∴ The value of ^αC₂ is .

If ²ⁿC₃ : ⁿC₂ = 44 : 3, find n.

If ¹⁶C_r = ¹⁶C_{r + 2}, find ^rC₄.

Prove that the product of 2n consecutive negative integers is divisible by (2n)!