You are 1 of 7 female candidates auditioning for 2 parts-the heroine and her best friend-in a play. Before the auditions you know nothing of the other candidates, and you assume all candidates have equal chances for the parts.
a. How many distinct choices are possible for casting the two parts?
b. In how many of the possibilities in part (a) would you be chosen to play the heroine?
c. In how many of the possibilities in part (a) would you be chosen to play the best friend?
d. Use the results in parts (a) and (b) to find the probability that you will be chosen to play the heroine. Indicate a more direct way of finding this probability.
e. Use the results in parts (a), (b), and (c) to find the probability that you will be chosen to play 1 of the 2 parts. Indicate a more direct way of finding this probability.