Probability/Law of Cosine?

Question

1. Theresa has 5 mysteries, 4 adventure stories, and three historical novels. She can choose 8 books for her summer reading.

A. What is the probability that an 8 book selection will contain 3 mysteries, 2 adventure stories, and 3 historical novels? Answer is 60/495. Don't know how though.

B. What is the probabilty that an 8 book selection will have no adventure books? Answer is 1/495

2. In triangle ABC a=4 b=3 and Cos C= -1/2 What is the length of c? I did x^2=4^2+3^2 - 2 times 4 times 3 times cos C=-1/2 but couldn't get the answer which was square root of 37.

Answer 1

1. Theresa has 5 mysteries, 4 adventure stories, and three historical novels. She can choose 8 books for her summer reading.

A. What is the probability that an 8 book selection will contain 3 mysteries, 2 adventure stories, and 3 historical novels?

(5C3)*(4C2)*(3C3) / (12C8) = 60/495 = 4/33

B. What is the probabilty that an 8 book selection will have no adventure books?

Divide the books into two types, adventure and non-adventure. There are 4 adventure and 8 non-adventure books.

(8C8) / (12C8) = 1/495

2. In triangle ABC a=4 b=3 and Cos C= -1/2 What is the length of c?

Using the Law of Cosines we have:

c² = a² + b² - 2ab cosC
c² = 4² + 3² - 2*4*3*(-1/2) = 16 + 9 + 12 = 37
c = √37

Answer 2

A.
5/12 * 4/11 * 3/10 * 4/9 * 3/8 * 3/7 * 2/6 * 1/5

B.
4^8/12!

I dont know jack about combinatorics or probability. I could very well be wrong about all this. But I do know trig fairly well, and the answer sqrt 37 is correct. You showed me the correct equation... I dont know why you didnt get it right. A basic arithmetic or algebraic error, probably