$1)$ How many different ways can $3$ red, $4$ yellow and $2$ blue bulbs be arranged in a row?
Do I just say $3! 4! 2! = 288$ ?
$2)$ On a shelf there are $4$ different math books and $8$ different English books.
a. If the books are to be arranged so that the math books are together, how many ways can this be done?
b. What is the probability that all the math books will be together?
For part $a)$, I put $8! 4! = 967680$ and part $b)$, $\dfrac{8!4!}{ 12!}$
I'm not too sure if i did these right and I would appreciate some help, thanks.