Find the value of `""^(10)C_(5) + 2* (""^(10)C_(4)) + ""^(10)C_(3)`.

Prove that ""^(10)C_(3)+""^(10)C_(6)=""^(11)C_(4)

If ""^(9)C_(3)+""^(9)C_(5)=""^(10)C_(r) then find r.

The value of ""^(40) C_(31) + sum _(r = 0)^(10) ""^(40 + r) C_(10 +r) is equal to

I : IF ""^(12)C_(r+1) ="" ^(12) C_(3r-5) then r=3 or 4 . II : If ""^(9) C_(3) +""^(9)C_(5) = ""^(10)C_(r) then r=4 or 6.

If 10. ""^(n)C_(2)=3. ""^(n+1)C_(3) find n.