Question

If ⁿP_r = 840, ⁿC_r = 35, then r = ______.

Answer 1

If ⁿP_r = 840, ⁿC_r = 35, then r = 4.

Explanation:

Given that ⁿP_r = 840 and ⁿC_r = 35

⇒ `(n!)/((n - r)!)` = 840  .....(i)

And `(n!)/(r!(n - r)!)` = 35  ....(ii)

Dividing equation (i) by equation (ii) we get

`((n!)/((n - r)!))/((n!)/(r!(n - r)!)) =840/35`

⇒ `(n!)/((n - r)!) xx (r!(n - r)!)/(n!)` = 24

⇒ r! = 24

⇒ r! = 4 × 3 × 2 × 1

⇒ r! = 4!

∴ r = 4

Hence the value of the filler is 4.