Question $4$:

A civil engineering team is preparing to start a small road construction project. The project

plan includes three main types of tasks: surveying, paving, and inspecting. There are $6$

surveying tasks, $3$ paving tasks, and $4$ inspecting tasks.

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

$($b$)$ Determine how many sequences have all surveying tasks, paving tasks, and inspecting

tasks grouped together.

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