A company has $25$interviewers for a empty position of receptionist manager, vice$-$receptionist, and $5$ members of the account team. The account team members are considered identical position.

$(1)$ How many ways can the position be filled from the $25$ applicant.

$(2)$ If $15$of the applicant has a PHD degree and the other $10$ has an associate degree, how many ways can the position be filled so that $5$ or more of the new employee have PHD degree. All $25$ interviewers are qualified for the $3$ types of position, irrespective of there degree.

$(3)$ Assume the receptionist manager is a boss to both the vice$-$receptionist and the account team, and the vice receptionist is a boss to the sales team. If one of the applicant Jacob, refuse to accept the job in which Davis is his boss. How many ways can the position be filled.