If `"^(18)C_r = ^(18)C_(r+2)`, find `"^(r )C_5`

If .^(15)C_(3r)=.^(15)C_(r+3), find .^(r)C_(2) .

If ""^(n)C_(r ): ""^(n)C_(r+1)=1:2 and ""^(n)C_(r+1): ""^(n)C_(r+2)=2:3 , find n and r.

If ([""^(n)C_(r) + 4*""^(n)C_(r+1) + 6*""^(n)C_(r+2)+ 4*""^(n)C_(r+3) + ""^(n)C_(r+4)])/([""^(n)C_(r) + 3. ""^(n)C_(r+1)+ 3*""^(n)C_(r+2) + ""^(n)C_(r +3)])=(n + lambda)/(r+lambda) the value of lambda is

If .^(n)C_(r )=84, .^(n)C_(r-1)=36 " and" .^(n)C_(r+1)=126 , then find the value of n.

The number of values of 'r' satisfying the equation ""^(39)C_(3r-1)- ""^(39)C_(r^(2) )= ""^(39)C_(r^(2)-1) - ""^(39)C_(3r) is

Prove that "^nC_r+2 ^(n)C_(r-1)+ ^(n)C_(r-2) = ^(n+2)C_r .

If "^(n-1)C_r : ^nC_r : ^(n+1)C_r= 6:9: 13 , find n and r.

If ^n-1C_r=(k^2-3)^n C_(r+1),then k in

If 10C_r=^10C_2 find the values of r.