^ 2 n C ₄: ^ n C ₃=99: 4 n =

Step-by-step solution

^ 2 n C₄: ^n C₃=99: 4 2 n ! 4 !(2 n-4) ! n ! 3 !(n-3) ! = 99 4 2 n (2 n -1)(2 n -2)(2 n -3) 4 n ( n -1)( n -2) = 99 4 2(2 n-1) 2(2 n-3) (n-2) =99 aligned & 4 (4 n^2-6 n-2 n+3 )=99 n-198 & 16 n^2-32 n+12=99 n-198 & 16 n^2-131 n+210=0 (n-6)(16 n-35)=0 & n-6=0 or 16 n-35=0 aligned n =6 or n = 35 16 (Not possible)