Explain the purpose of the survey or study

• Identify the source of the bias

• How did the bias affect the results?

• What were the consequences of the flawed findings?

• How might the process have been improved to minimize the possibility of bias?

8 marks

• Use Robert Harris’s article http://www.virtualsalt.com/evalu8it.htm

to answer the following questions:

a. Why is print material considered more credible than Internet material?

b. According to Robert Harris what kind of information exists on the internet?

c. What tip does Robert Harris offer to determine if a source is reliable/credible?

d. Summarize the CARS checklist. Include important questions you must ask yourself and indicators of poor information when evaluating an Internet set for each of the topics.

e. How can you tell the motivation and source of a document from the Internet address?

5 marks

A committee of 5 people is to be chosen from a group of 8 women and 10 men.

. How many diffferent committees are possible?

a. 18x17x16x15x14= 1,028,160/5! = 2,391.07

***How many are possible if the following restrictions are enforced;

b. The committee must feature both men and women?

8x10x16x15x14= 268,800

c. The committee must feature 3 women and two men?

8x7x6x10x9=30,240

d. The committee must have more women than men?

8x7x6x10x9 = 30,240

+

8x7x6x5x10=16,800

+

8x7x6x5x4= 6,720

=53,760

8 marks

A baseball team has 14 players.

How many 9-person batting orders are possible? 14x13x12x11x10x9x8x7x6x5=6,572,966,400/9!=18,113.33

.

a. How many batting orders are possible if Schierholtz is always in the starting line-up and always bats fourth?

13x12x11x1x10x9x8x7x6= 51,891,840 / 8! = 1,287

4 marks

Consider the word MATHEMATICS.

. How many arrangements are there of the word MATHEMATICS?

a. 11!/2!x2!x2!= 39,916,800/8= 4,989,600

b. How many of these start with the letter M? 2x10x9x8x7x6x5x4x3x2x1=????

c. How many of the arrangements in part a have the T’s together?*********

6 marks

We have looked at situations in which we need to determine the number of possible routes between two places. We can look at the situation below as 9 steps, six of which must be East and three of which must be South.

This gives us 9! = 84 possible routes

3!6!

The calculation 9! is equivalent to 9C3 (or 9C6)

3!6!

Explain clearly why you could solve this question using combinations, and why this is equivalent to considering permutations with repeated items.

We would use combinations because the order in which you travel does not matter. Permutations with repeated items could be used because we multiple steps south and multiple steps east but combinations in the case work because order does not matter and we must eliminate repeated combinations.

4 marks

There are 8 parents and 43 students going on a school trip. Two groups are made, a large one with thirty students and five parents, and a small group with 13 students and three parents.

<li >

How many different ways can be the parents be chosen for the small group?

How many ways can the students be chosen for the large group if Stefan and Dylan must be in the small group?

How many ways can the groups be arranged if Reena and both her parents must be in the small group?

6 marks

• Simplify each expression and write it without using factorial notation.

a. (n + 4)! nPn+4 or

n+4xn+3xn+2xn+1

(n + 2)! nPn+2 or

n+2xn+1

b. (n – r + 1)!

(n – r – 2)!

•

6 marks

• Investigate a lottery competition somewhere in the world. Explain how the lottery works, and what needs to happen for someone to win the jackpot, and at least one of the minor prizes.

Lottery Balls

Calculate the probability of winning each of the prizes you described, giving a full explanation of your work.

Consider the cost of playing. Do you think the prizes on offer are fair? If not, why not, and why do you think people continue to play?

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