If ^n C_ r-1 =36, ^n C_r=84 and ^n C_ r+1 =126 , then the value of n r^2 is

Step-by-step solution

^n C_r ^n C_ r-1 = 84 36 n ! (n-r) ! r ! n ! (r-1) !(n-r+1) ! = 7 3 array ll & n-r+1 r = 7 3 & 3 n-3 r+3=7 r array 3 n+3=10 r (i) Again, ^n C_ r+1 ^n C_r = 126 84 array ll & n-r r+1 = 3 2 & 2 n-2 r=3 r+3 array 2 n-3=5 r ...(ii) Dividing Eq. (i) by Eq. (ii) 3 n+3 2 n-3 = 10 r 5 r =2 3 n+3=4 n-6 n=9 From Eq. (i), 3 9+3=10 r r=3 n r^2=9 9=81