Math 1332 Extra Credit Problems(Due with Final Exam)

Given an old dog, a young boy, a string, and a tin can, what’s the

probability that the can will get tied to the dog’s tail? Match your answer to the following probability questions with the correct lettered answers below, and place the letter in

the corresponding box at the bottom to get the answer to the riddle.

A box contains 2 blue, 3 green, and 10 red marbles. One marble is drawn at random from the box.

1) What is the probability that the marble is green?

2) What is the probability that the marble is not red?

3) What is the probability that the marble is white?

4) What is the probability that the marble is blue or green or red?

In a class of 4 boys and 6 girls, each writes his/her name on a piece of paper and puts it into a hat. Two

pieces of paper are randomly drawn from the hat without replacement.

5) What is the probability that both are girls’?

6) What is the probability that one is a boy and one is a girl?

In a class of 4 boys and 6 girls, each writes his/her name on a piece of paper and puts it into a hat. Two

pieces of paper are randomly drawn from the hat with replacement.

7) What is the probability that both are girls’?

8) What is the probability that one is a boy and one is a girl?

Two fair dice are tossed.

9) What is the probability that the sum is 7?

10) What is the probability of not getting a double?

11) What is the probability of a sum of seven or getting a double?

12) What is the probability that the sum is less than 5?

13) What is the probability that the sum is less than 13?

Three fair coins are tossed.

14) What is the probability of getting two heads and one tail?

15) What is the probability of getting one head and two tails?

Three married couples are in a room, and two people are chosen at random without replacement.

16) What is the probability that one is a male and one is a female?

17) What is the probability that both are male?

18) What is the probability that the two people are married to each other?

19) What is the probability that the two people are not married to each other?

20) What is the probability that the two people are either of the same gender or opposite gender?

A. 0 B. 925 C. 1225

D. 56

E. 38

F. 18

G. 135

I. 35 K. 1

30 L. 2

15 M. 1

36 N. 1 O. 15 P.

19

R. 45 S. 8

15 T. 13 U.

16 V.

17 W.

1835 Y.

12

‘ ,

16 5 6 17 4 14 6 16 13 8 15

‘

16 2 6 7 18 9 20 10 11 1 3 8 12 19

Why should you never let a mathematician set your hair? Match your answers to the following problems with the lettered answers below, and write the letter in

the corresponding box at the bottom to get the answer to the riddle.

1) 7 3P 2) 7 4P 3) 7 3C 4) 7 4C 5) 4 7P

6) 7 7P 7) 7 7C 8) 7 1P 9) 7 1C 10) 7 0C

A. 1 B. 6 E. 210 M. 35 N. 343

O. 5040 P. 24 T. 7 U. 840 W. 823,543

X. 2401 Y. 0 A. 35 C. 53 E. 55

G. 5! I. 24! K. 10! M. 5 3P N. 5 3C

O. 5!

3! P.

10!

3! 3! 2! R. 24 3P T. 24 3C U. 14 3 10 3C C

Y. 14 3 10 3C C

5 21 18 3 10 19 11 1 9

7 22 12 16 4 13 2 17 14 8 20 6 15

11) How many permutations of the letters VWXYZ are there?

12) How many different 5-letter words with repetition can be formed from the letters VWXYZ?

13) How many different 3-letter words without repetition can be formed from the letters

VWXYZ?

14) How many different 3-letter words with repetition can be formed from the letters VWXYZ?

15) How many different subsets of size three are there from the set , , , ,V W X Y Z ? 16) In a class of 24 students, how many ways could a first, second, and third prize be awarded if

no student can be awarded more than one prize?

17) In a class of 24 students, how many different committees of size 3 can be chosen?

18) In a class of 14 boys and 10 girls, how many different committees of size 6 consisting of 3

boys and 3 girls can be chosen?

19) In a class of 14 boys and 10 girls, how many different 3-person committees are of the same

gender?

20) How many different ways can a class of 24 students line up?

21) How many different permutations of the letters in the word DADDY are there?

22) How many different permutations of the letters in the word STATISTICS are there?

What’s the first line of the famous poem in which the author declares her

feelings for her combinatorics teacher? Match your answers to the following counting problems with the lettered answers below, and write the

letter in the corresponding box at the bottom to get the answer to the riddle.

1) How many male/female couples can be formed with 5 boys and 7 girls?

2) How many different outfits can be mixed and matched with 8 shirts and 3 pairs of pants?

3) How many different outfits can be mixed and matched with 8 shirts, 3 pairs of pants, and 2

jackets?

4) How many different ways can the letters in the word AID be arranged?

5) How many different ways can the letters in the word ADD be arranged?

Using any of the letters W, X, Y, and Z only once,

6) How many different four-letter words can be formed?

7) How many different three-letter words can be formed?

8) How many different four-letter words can be formed if repeated letters are allowed?

9) How many three-digit numbers are there? (025 isn’t a three-digit number)

10) How many odd three-digit numbers are there?

11) How many even three-digit numbers are there?

12) How many three-digit numbers that are multiples of 5?

13) How many three-digit numbers are there if repeated digits are not allowed?

14) In how many different ways can 7 people line up?

15) In how many different ways can 7 people line up if one particular person has to stand at the

head of the line?

16) In how many different ways can a president and vice-president be chosen from 7 people?

17) In how many different ways can 4 Americans and 3 Russians be seated in a row so that

those from the same country sit together?

18) When rolling two dice, how many different outcomes are possible?

19) When rolling two dice, how many different ways can the sum be 4?

20) When rolling two dice, how many different ways can the sum be 7?

21) When rolling two dice, how many different ways can you roll a double?

22) When tossing 3 coins, how many ways can you get 3 heads?

23) When tossing 3 coins, how many ways can you get 2 heads and 1 tail?

24) When tossing 3 coins, how many ways can you get 1 head and 2 tails?

25) When tossing 3 coins, how many ways can you get neither all heads nor all tails?

A. 1 B. 12 C. 48 D. 35 E. 3 F. 10 H. 24

I. 256 K. 16 L. 288 M. 42 N. 180 O. 6 P. 100

R. 500 S. 36 T. 450 U. 648 V. 720 W. 900 Y. 5040

? 7 20 9 1 21 8 17 4 15 23 11 2 24 24

17 5 10 16 19 3 25 13 12 10 11 6 5 9 22 14 18

How do you turn the set ,arms legs into the empty set? Given the following sets, find each intersection or union as requested. Note: Some of the unions and

intersections are given in terms of the original sets. Match your answer with the lettered answers

below, and place the letter in the corresponding box at the bottom of the page to get the answer to the

riddle.

4, 2,0,2,4A , 5, 3, 1,0,1,3,5B , 5, 4, 3, 2, 1,0C , 0,1,2,3,4,5D

1) A B 2) A C 3) C D 4) A B

5) C D 6) A D C 7) C D A 8) A D A B

2,4,6,8,A , 1,3,5,7,B , 3,6,9,12,C , 5,10,15,20,D

9) A B 10) C D 11) A B 12) A C

0,1,2,3,A , 0, 1, 2, 3,B , 1 1 12 3 4, ,C , , 3, 2, 1,0,1,2,3,D

13) A B 14) A B 15) A D 16) C D

17) A B 18) B C 19) B C 20) A C B

I. A B. B G. C N. D

M. 0 E. or L. 1,2,3,4,5 O. 1,2,3,4,

R. 4, 2,0 T. 0,2,4 S. 5, 4, 3, 2, 1,0,1,2,3,4,5 V. 15,30,45,60,

Y. 6,12,18,24, Z. 0,4,8,12,

19 12 6 9 1 11 10 15 14 18

7 8 4 13 17 3 20 16 2 5

A B

C

U

Starting on the left at 10, you choose a path always moving to the right until you get to the Finish.(Do

not follow the order of operations, just calculate as you go!)

What’s the largest possible result?

What’s the smallest possible result?

Starting on the left at 2, you choose a path always moving to the right until you get to the Finish. (Do

not follow the order of operations, just calculate as you go!)

What’s the largest possible result?

What’s the smallest possible result?

Starting on the left at 50, you choose a path always moving to the right until you get to the Finish. (Do

not follow the order of operations, just calculate as you go!)

What’s the largest possible result?

What’s the smallest possible result?

Starting on the left at 100, you choose a path always moving to the right until you get to the Finish. (Do

not follow the order of operations, just calculate as you go!)

What’s the largest possible result?

What’s the smallest possible result?

6 2 8 4 5

6

1 8

3

9 2

6 2 8 4 5

6