If nPr = 840 and nCr = 35, find the value of r.

Given: nPr = 840 and nCr = 35To find: r=?We know that:nCr =andnPr =⇒ nPr= nCr×r!⇒840=35×r!⇒⇒r!=4!⇒r=4Ans:r=4

Q8 of 68 Page 330

If ⁿP_r = 840 and ⁿC_r = 35, find the value of r.

Given: ⁿP_r = 840 and ⁿC_r = 35

To find: r=?

We know that:

ⁿC_r =

and

ⁿP_r =

⇒ ⁿP_r= ⁿC_r×r!

⇒840=35×r!

⇒

⇒r!=4!

⇒r=4

Ans:r=4

If ²ⁿC₃: ⁿC₃ = 12 : 1, find n.

If ¹⁵C_r : ¹⁵C_r–1 = 11 : 5, find r.

If ⁿC_r–1 = 36, ⁿC_r = 84 and ⁿC_r+1 = 126, find r.

If ⁿ⁺¹C_r+1 : ⁿC_r = 11 : 6 and ⁿC_r : ^n–1C_r–1 = 6 : 3, find n and r.