This is equivalent to say Distribution of 50 non-distinct coins into 3 distinct people where each people gets atleast 5 coins.
First, distribute 5 coins to each people.Then the number of coins left is 35.Then Distribute 35 coins to 3 peoples arbitrarily.
So, total no of ways of Distributing 35 coins to 3 peoples arbitrarily (i.e people get 0 or more coins) = C(3+35-1, 35) = C(37, 35) = C(37, 2) = 666
The correct answer is,(E) C(37, 2)