Whats the easiest way to approach questions like this?
Part (c) in particular.
Is the first answer 10c4 * 3^4 and last one 15c4 * 4c4?
Please can someone confirm?
use the binomial theorem
$(a + b)^n = \sum \limits_{k=0}^n~\dbinom{n}{k}~a^k~b^{n-k}$
$(3x+y)^{10} = \sum \limits_{k=0}^{10}~\dbinom{10}{k}~(3x)^k~y^{10-k}$
we are clearly looking for the term that corresponds to $k=4$ which is
$\dbinom{10}{4}~3^4 x^4 y^6$
and thus the coefficient is
$\dbinom{10}{4}~3^4 = 17010$
use the same method on (b) and (c)
In the expansion of ${(x + y + 3)^{15}}$
we have ${\dbinom{15}{5}}{(x + y)^{10}}{(3)^5}$
$ {\dbinom{15}{5}} \cdot {\dbinom{10}{4}}{y^{10 - 4}}{x^4}{(3)^5}$
You should get $153243090$ see HERE