Six jurors are to be selected from a pool of $20$ potential candidates to hear a civil case involving a lawsuit between two families.

Unknown to the judge or any of the attorneys, $4$ of the $20$ prospective

jurors are potentially prejudiced by being acquainted with one or more

of the litigants. They will not disclose this during the jury selection process. If $6$ jurors are selected at random from this group of $20,$ find

the probability that the number of potentially prejudiced jurors among

the $6$ selected jurors is

a$.$ exactly $1$ b$.$ none c$.$ at most $2$