What is the value of n , if P(15, n-1): P(16, n-2)=3: 4 ?

Step-by-step solution

aligned & P (15, n-1): P (16, n-2)=3: 4 & 15 P _ n-1 16 P _ n-2 = 3 4 aligned 15! 15-x+1! 16! (16-n+2) = 3 4 15!18-n! 16!16-n! = 3 4 aligned & (8-n)(17-n) 16 = 3 4 & n^2-35 n+294=0 & n^2-21 n-14 n+294=0 & n(n-21)-14(n-21)=0 aligned n=14,21 .