Please answer the following. if one could show work. I’d very much apperciate it.
1. (30 pts) A survey of 80 college students was taken to determine the musical styles they listened to. Forty-two students listened to rock, 34 to classical, and 27 to jazz. Twelve students listened to rock and jazz, 14 to rock and classical, and 10 to classical and jazz. Seven students listened to all three musical styles. Of those surveyed,
a. How many listened to only rock music?
b. How many listened to classical and jazz, but not rock?
c. How many listened to classical or jazz, but not rock?
d. How many listened to music in exactly one of the musical styles?
e. How many listened to music in at least two of the musical styles?
f. How many did not listen to any of the musical styles?
2. (20 pts) There are four blood types, A, B, AB, and O. Blood can also be Rh+ and Rh-. Finally, a blood donor can be classified as either male or female. How many different ways can a donor have his or her blood labeled? (Use tree diagram)
3. (20 pts) In a club there are 7 women and 5 men. A committee of 3 women and 2 men is to be chosen. How many different possibilities are there?