Question

n-1P3 : n+lP3 = 5:12​

Answer 1

As we know,

nPr = n!/ (n−r)!

n−1 (P) 3 : n+1( P) 3 =5:12

⇒( (n−1)!/(n-4)!) /((n+1)!/ (n−2)!) = 5/12

⇒ (n−1)(n−2)(n−3)/(n+1)n(n−1) = 5/12

⇒12(n−2)(n−3)=5(n+1)n

⇒7n^2−65n+72=0

⇒7n^2−56n−9n+72=0

⇒7n(n−8)−9(n−8)=0

⇒(n−8)(7n−9)=0

⇒n=8.