Find r if `.^(18)C_r = 6"^(18)C_(r+2)`

Find r if "^5P_r = "^6P_(r-1) .

Find r if "^5P_r =2 "^6P_(r-1) .

Find r if : ^5P_r= "^6P_(r-1) .

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

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

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

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