Thirteen graduate students have applied for four available teaching assistantships. In how many ways can these assistantships be awarded among the applicants if (a) No preference is given to any one...

(a) No preference is given to any one student?
 ways


(b) One particular student must be awarded an assistantship?
 ways


(c) The group of applicants includes seven men and six women and it is stipulated that at least one woman must be awarded an assistantship?
 ways