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.