Question

Please explain how you got your answers! (: Solve the problem by using the counting principle.

A. Drapery is sold in 4 different fabrics. Each fabric comes in 13 different patterns. Each pattern is offered in 9 different colors. How many fabric-pattern-color combinations are there?

B. A shelf hold 3 novels, 2 biographies, and 1 history book. Two students in turn choose a book at random. What is the probability that the student choose the following?
both novels

A. 1/4
B. 1/2
C. 1/5
D. 1/3

A shelf hold 3 novels, 2 biographies, and 1 history book. Two students in turn choose a book at random. What is the probability that the student choose the following?

both biographies

A. 1/15
B. 1/20
C. 1/5
D. 1/3

A shelf hold 3 novels, 2 biographies, and 1 history book. Two students in turn choose a book at random. What is the probability that the student choose the following?

a history, then a novel

A. 1/2
B. 1/5
C. 1/10
D. 1/15

Answer 1

A. The number of fabric-pattern-color combinations is 4 * 13 * 9 = 468

B. P(1st choice) = no of novels / total books = 3/6 = 1/2
P(2nd choice) = no of remaining novels/ total remaining books = 2/5
P(both novels) = 1/2 * 2/5 = 1/5 (without replacement assumed)

C. P(1st choice) = no of biographies / total books = 2/6 = 1/3
P(2nd choice) = no of remaining biographies/ total remaining books = 1/5
P(both biographies) = 1/3 * 1/5 = 1/15 (without replacement assumed)

D. P(1st choice) = no of history books / total books = 1/6
P(2nd choice) = no of novels/ total remaining books = 3/5
P(a history, then a novel) = 1/6 * 3/5 = 1/10 (without replacement assumed)