1. In how many different ways can the letters in the word STUDY be ordered?

2. Martha invited 4 friends to go with her to the movies. There are 120 different ways in which they can sit together in a row of 5  seats, one person per seat. In how many of those ways is Martha sitting in the middle seat?

3.  How many 3-digit positive integers are odd and do not contain the digit 5 ?

4. From a box of 10 lightbulbs, you are to remove 4. How many different sets of 4 lightbulbs could you remove?

5.  A talent contest has 8 contestants. Judges must award prizes for ﬁrst, second, and third places, with no ties.

(a) In how many different ways can the judges award the 3 prizes?
(b) How many different groups of 3 people can get prizes?

6. If an integer is randomly selected from all positive 2-digit integers, what is the probability that the integer chosen has

(a) a 4 in the tens place?
(b) at least one4 in the tens place or the units place?
(c) no 4 in either place?

7. There are 5 doors to a lecture room. Two are red and the others are green. In how many ways can a lecturer enter the room and leave the room from different colored doors?

(A) 1
(B) 3
(C) 6
(D) 9
(E) 12

8. Four pool balls—A, B, C, D—are randomly arranged in a straight line. What is the probability that the order will actually be A, B, C, D ?

(A) 1/4
(B) \frac { 1 }{ { _{ 4 }{ C }_{ 4 } } }
(C) \frac { 1 }{ { _{ 4 }{ P }_{ 4 } } }
(D) 1/2!
(E) 1/3!

9.  A basketball team has 11 players on its roster. Only 5 players can be on the court at one time. How many different groups of 5 players can the team put on the floor?

(A) { 5 }^{ 11 }
(B) { _{ 11 }{ C }_{ 5 } }
(C) { _{ 11 }{ P }_{ 5 } }
(D) { 11 }^{ 5 }!
(E) 11!*5!

10. This is how Edward’s Lotteries work. First, 9 different numbers are selected. Tickets with exactly 6 of the 9 numbers randomly selected are printed such that no two tickets have the same set of numbers. Finally, the winning ticket is the one containing the 6 numbers drawn from the 9 randomly. There is exactly one winning ticket in the lottery system. How many tickets can the lottery system print?

(A) { _{ 9 }{ P }_{ 6 } }
(B) { _{ 9 }{ P }_{ 3 } }
(C) { _{ 9 }{ C }_{ 9 } }
(D) { _{ 9 }{ C }_{ 6 } }!
(E) { 6 }^{ 9 }

11.  How many different strings of letters can be made by reordering the letters of the word SUCCESS?

(A) 20
(B) 30
(C) 40
(D) 60
(E) 420

12.   A 10-student class is to choose a president, vice president, and secretary from the group. Assuming that no person can occupy more than one post, in how many ways can this be accomplished?

13.

 Quantity A Quantity B The number of 4-digit positive integers where all 4 digits are less than 5 625

14.  A state issues automobile license plates using two letters selected from a 26-letter alphabet, as well as four numerals selected from the digits 0 through 9, inclusive. Repeats are permitted. For example, one license plate combination could be GF3352.

 Quantity A Quantity B The number of possible unique license plate combination 6,000,000

15. A small nation issues license plates that consist of just one number (selected from the digits 0 through 9, inclusive) and four letters, selected from a 20-letter alphabet. Repeats are permitted. However, there is one four-letter combination that is not allowed to appear on license plates. How many allowable license plate combinations exist?

(A) 1,599,990
(B) 1,599,999
(C) 1,600,000
(D) 4,569,759
(E) 4,569,760

1  5!=120
2 24
3 288
4 210
5 (a) 336 (b) 56
6 (a) 1/9    (b) 1/5    (c)4/5
7 E
8 C
9 B
10 D
11 E
12 720
13 B
14 A
15 A