Kelly has different books to arrange on a shelf; $2$ blue, $4$ green, and $3$ red. Answer parts a through e below.

$($a$)$ In how many ways can the books be arranged on a shelf?

way$($s$)$

$($Type a whole number.$)$

$($b$)$ If books of the same color are to be grouped together, how many arrangements are possible?

way$($s$)$

$($Type a whole number.$)$

$($c$)$ In how many distinguishable ways can the books be arranged if books of the same color are identical but need not be grouped together.

way$($s$)$

$($Type a whole number.$)$

$($d$)$ In how many ways can you select $3$ books, one of each color, if the order in which the books are selected does not matter.

way$($s$)$

$($Type a whole number.$)$

$($e$)$ In how many ways can you select $3$ books, one of each color, if the order in which the books are selected matters.

way$($s$)$

$($Type a whole number.$)$