As a volunteer activity, 10 students want to put on a talent show at a retirement home.  To organize the show, 3 of these students will be chosen at random to form a committee.  Victoria really wants to be on this committee, since her grandmother lives at the home.  Each student's name will be written on a slip of paper and placed in a hat.  Then 3 names will be drawn.

a) What is the likelihood that Victoria's name will be drawn from the hat?

c) In how many different ways can 3 names be drawn from a hat with 10 names?

d) In how many different ways can Victoria's name be drawn with 2 other names?

e) What is the probability that Victoria's name will be drawn?

Please show your steps and explain.