If nCr–1 = nC3r, find r.

Given: nCr–1 = nC3rTo find: r=?We know that:nCr = nCn-r⇒ nCr–1 = nCn-(r-1)⇒ nCr–1 = nCn-r+1⇒ nCn-r+1= nC3r⇒n-r+1=3r⇒4r=n+1⇒Ans:

Q5 of 68 Page 330

If ⁿC_r–1 = ⁿC_3r, find r.

Given: ⁿC_r–1 = ⁿC_3r

To find: r=?

We know that:

ⁿC_r = ⁿC_n-r

⇒ ⁿC_r–1 = ⁿC_n-(r-1)

⇒ ⁿC_r–1 = ⁿC_n-r+1

⇒ ⁿC_n-r+1= ⁿC_3r

⇒n-r+1=3r

⇒4r=n+1

⇒

Ans:

(i) If ⁿC₇ = ⁿC₅, find n.

(ii) If ⁿC₁₄ = ⁿC₁₆, find ⁿC₂₈.

(iii) If ⁿC₁₆ = ⁿC₁₄, find ⁿC₂₇.

(i) If ²⁰C_r = ²⁰C_r+6, find r.

(ii) If ¹⁸C_r = ¹⁸C_r+2, find ^rC₅.

If ²ⁿC₃: ⁿC₃ = 12 : 1, find n.

If ¹⁵C_r : ¹⁵C_r–1 = 11 : 5, find r.