A software development team is planning to complete a new project that includes four types of tasks:

$6$ coding tasks, $5$ debugging tasks, $4$ user testing tasks, and $3$ documentation tasks.

$($a$)$ Calculate the total number of possible sequences for scheduling all these tasks.

$($b$)$ Determine how many sequences have all coding tasks, debugging tasks, user testing tasks, and documentation tasks grouped together $($i$.$e$.,$ all coding tasks are together, all debugging tasks are together, all user testing tasks are together, and all documentation tasks are together$)$

$($c$)$ Find how many schedules can start and end with a coding task.