# probability and statistics counting methods

1.Use your calculator to evaluate 8C5

Enter your answer into the box below (if the answer is large, do not use spaces or commas)

2.How many different ways can seven different cans of soda be displayed on a shelf?

Select one:

A. 7

B. 1

C. 7!

D. None of these

E. 2

3.You are at the pet store and decide to purchase 3 fish from a particular aquarium. You notice that there are currently 12 fish in the aquarium. How many different sets of fish can end up traveling home with you?

Select one:

A. 1320

B. 479,001,600

C. 6

D. 220

4.A bag contains 1 brown rock, 1 gray rock, and 1 red rock. Two rocks are drawn from the bag, one after the other, without replacing the previous rock. How many different outcomes will be in the sample space if the order of the rocks matters?

Enter your solution into the box below. Be sure that you enter a number (not a factorial or a formula). If your answer is large, do not use spaces or commas.

5.You have been hired to crack a code on a super-secret safe. The code consists of two letters followed by three numbers. How many possible secret codes are there if digits and letters can be repeated in the code?

Select one:

A. 260

B. 82

C. 1,560

D. 468,000

E. 676,000

6.A bag contains many different colored marbles. In fact you know the following …
1. The bag contains purple, black, white, and maroon marbles.
2. You will draw two marbles out of the bag (one after the other).
3. You will never draw the same colored marbles.

Which of the following is the correct sample space for what might occur?

Select one:

A. S={P,B}

B. S={PB,PW,PM,BP,BW,BM,WP,WB,WM,MP,MB,MW}

C. S={P,B,W,M}

D. S={PP,PB,PW,PM,BB,BP,BW,BM,WW,WP,WB,WM,MM,MP,MB,MW}

7.A cross-country running coach needs to select four runners to compete in an upcoming cross-country race. There are currently six sophomores and four juniors available for this race. How many teams of four runners are available for the race if the team must include two sophomores and two juniors?

Select one:

A. 90

B. 210

C. 96

D. 2,025

E. 15

F. 360

8.The flower shop has ten different flower arrangements. How many different ways can the shop show flowers if their display case can hold three flower arrangements and no flower arrangement is repeated?

Select one:

A. 10!

B. 120

C. 6

D. 720

9.Complete the following
Count how many of the following items you personally own (if you are not at home right now, use your best estimate):

Pairs of shoes
Pairs of long pants
Sweatshirts

In the text box below, state how many of each you own and then find how many different outfits you can make from what you own (an outfit consists of one pair of shoes, one pair of pants, and one sweatshirt). Be sure to explain exactly how you got your answer.

Important Note:
This problem will be scored as zero points until your teacher manually grades it.
Your exam score will be changed once your instructor checks this problem.

10.If you roll a 4-sided die and a 6-sided die at the same time and then add the result on each of the dice, how many different ways can you get a number greater than 7?

Select one:

A. 6

B. 24

C. 3

D. 10

11.In how many ways can you arrange the letters in the word MATH ?

Select one:

A. 12

B. 4

C. 10

D. 24