If `"^(n)C_8 `= `"^(n)C_2`. Find `"^(n)C_2`

Find n, if ""^(2n)C_(1),""^(2n)C_(2) and ""^(2n)C_(3) are in A.P.

If ""^(n)C_(3) + ""^(n)C_4 gt ""^(n+1) C_3 , then.

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_(9)=.^(n)C_(7) , find n.

If "^(2n)C_3 : ^nC_2= 12: 1 , find n .

if .^(2n)C_(2):^(n)C_(2)=9:2 and .^(n)C_(r)=10 , then r is equal to

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

Prove that .^(n)C_(0) + (.^(n)C_(1))/(2) + (.^(n)C_(2))/(3) + "……" +(. ^(n)C_(n))/(n+1) = (2^(n+1)-1)/(n+1) .