By the binomial theorem,

I assume you meant to say "independent", not "indecent", meaning we're looking for the constant term in the expansion. This happens for k such that
12 - 3k = 0 ===> 3k = 12 ===> k = 4
which corresponds to the constant coefficient

I think it can be 605. I'm not sure exactly, but I think it is.
The answer to the question
Paul owes paula 35 cents...she has a pocket full of nickels,dimes,and quarters.
largest number of coins would be : 7 nickels (7 coins)
smallest number of coins would be : 1 quarter and 1 dime (2 coins)
the difference is : 7 - 2 = 5 coins <=
8 out of 24 = 1 out of 3
5 out of 20 = 1 out of 4
1/3 is larger that 1/4
Jessica has the largest ratio