Math 378 Name________________

Final Exam

Spring 2003 Show all Work

1) a) How many positive two-digit integers are multiples of 3?

12 …………. 99

3 * 4 ……… 3 * 33 answer: 33 - 4 + 1 = 30

b) What is the probability that a randomly chosen positive two-digit integer is a multiple of 3?

number of two digits numbers = 99 - 10 + 1 = 90

P(2 digit integer multiple of 3) = 30/90 = 1/3

2) What is the probability of rolling an 8 when two dice are rolled?

6*6 = 36 total possible rolls.

You can get an 8 with (2,6), (6,2), (3,5), (5,3) and (4,4)

P(rolling an 8) = 5/36

3) A person buying a personal computer system is offered a choice of six models of the basic unit, three models of a monitor, and four models of a printer. How many distinct systems can be purchased?

6*3*4 = 72

4) a) How many ways can the letters of the word COMPUTER be arranged in a row?

8!

b) How many ways can the letters of the word COMPUTER be arranged in a row if the letters COM must remain together (in order) as a unit?

6!

c) How many ways can four of the letters of the word COMPUTER be selected and written in a row?

8*7*6*5 = 1680 or (order matters)

d) How many ways can four of the letters of the word COMPUTER be selected and written in a row if the first two letters must be PR (in that order).

6 * 5 (6 ways to choose third letter, 5 ways to choose 4^th - order matters)