if n =1680 and n = 70, find n and r

P C

r r

Given : ⁿP_r = 1680, ⁿC_r = 70

Now, we know that r = ⁿP_r / ⁿC_r = 1680/70 =24 = 4!

⇒ r = 4

Also, ⁿP_r = n(n - 1)(n - 2)(n - 3) = 1680 = 8 × 7 × 6 × 5 = 8(8 - 1)(8 - 2)(8 - 3)

⇒ n = 8