In the first year after its release, 83 percent of emergency room doctors were estimated to have tried Dermabond glue (an alternative to sutures in some situations). (a) What kind of probability is this? (b) How was it probably estimated? (c) Why might the estimate be inaccurate? (Data are from Modern Healthcare 29, no. 32 [August 9, 1999], p. 70.)

A survey showed that 44 percent of online Internet shoppers experience some kind of technical failure at checkout (e.g., when submitting a credit card) after loading their shopping cart. (a) What kind of probability is this? Explain. (b) What are the odds for a technical failure? (See J. Paul Peter and Jerry C. Olson, Consumer Behavior and Marketing Strategy, 7th ed. [McGraw-Hill-Irwin], p. 278.)

A real estate office has 10 sales agents. Each of four new customers must be assigned an agent. (a) Find the number of agent arrangements where order is important. (b) Find the number of agent arrangements where order is $not$ important. (c) Why is the number of combinations smaller than the number of permutations?

A die is thrown $(1,2,3,4,5,6)$ and a coin is tossed $(H, T)$. (a) Enumerate the elementary events in the sample space for the die/coin combination. (b) Are the elementary events equally likely? Explain.

Define $odds$ . What does it mean to say that odds are usually quoted against an event?

Find the following combinations ${ }_n C_r$ :

a. $n=8$ and $r=3$.

b. $n=8$ and $r=5$.

c. $n=8$ and $r=1$.

d. $n=8$ and $r=8$.

Find the following permutations ${ }_n P_r$ :

a. $n=8$ and $r=3$.

b. $n=8$ and $r=5$.

c. $n=8$ and $r=1$.

d. $n=8$ and $r=8$

(a) In how many ways could you arrange seven books on a shelf? (b) Would it be feasible to list the possible arrangements?

Bob has to study for four final exams: accounting $(A)$, biology $(B)$, communications $(C)$, and drama $(D)$. (a) If he studies one subject at a time, in how many different ways could he arrange them? (b) List the possible arrangements in the sample space.

Until 2005, the UPC bar code had 12 digits (0–9). The first six digits represent the manufacturer, the next five represent the product, and the last is a check digit. (a) How many different manufacturers could be encoded? (b) How many different products could be encoded? (c) In 2005, the EAN bar code replaced the UPC bar code, adding a 13th digit. If this new digit is used for product identification, how many different products could now be encoded?

At Oxnard University, a student ID consists of two letters (26 possibilities) followed by four digits (10 possibilities). (a) How many unique student IDs can be created? (b) Would one letter followed by three digits suffice for a university with 40,000 students? (c) Why is extra capacity in student IDs a good idea?

American Express Business Travel uses a six-letter record locator number (RLN) for each client’s trip (e.g., KEZLFS). (a) How many different RLNs can be created using capital letters (A–Z)? (b) What if they allow any mixture of capital letters (A–Z) and digits (0–9)? (c) What if they allow capital letters and digits but exclude the digits 0 and 1 and the letters O and I because they look too much alike?

In the Minnesota Northstar Cash Drawing you pick five different numbers between 1 and 31. What is the probability of picking the winning combination (order does not matter)? $Hint$ : Count how many ways you could pick the first number, the second number, and so on, and then divide by the number of permuations of the five numbers.

(a) Find 7! without a calculator. Show your work. (b) Use your calculator to find 14! (c) Type 70! in the Google search window and record the answer (d) Which method, do you prefer? Why?