Identity Theft with Credit Cards Credit card numbers typically have 16 digits, but not all of them are random.


a. What is the probability of randomly generating 16 digits and getting your MasterCard number?

Corporate Officers and Committees The Self Driving Unicycle Company was recently successfully funded via Kickstarter and must now appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO), and chief human resources officer (CHR). It must also appoint a strategic planning committee with five different members. There are 15 qualified candidates, and officers can also serve on the committee.

b. How many different ways can a committee of five be appointed?

ATM You want to obtain cash by using an ATM, but it’s dark and you can’t see your card when you insert it. The card must be inserted with the front side up and the printing configured so that the beginning of your name enters first.

a. What is the probability of selecting a random position and inserting the card with the result that the card is inserted correctly?

ATM You want to obtain cash by using an ATM, but it’s dark and you can’t see your card when you insert it. The card must be inserted with the front side up and the printing configured so that the beginning of your name enters first.

c. How many random selections are required to be absolutely sure that the card works because it is inserted correctly?

Is the Researcher Cheating? You become suspicious when a genetics researcher “randomly” selects numerous groups of 20 newborn babies and seems to consistently get 10 girls and 10 boys. The researcher claims that it is common to get 10 girls and 10 boys in such cases.

a. If 20 newborn babies are randomly selected, how many different gender sequences are possible?

Phase I of a Clinical Trial A clinical test on humans of a new drug is normally done in three phases. Phase I is conducted with a relatively small number of healthy volunteers. For example, a phase I test of bexarotene involved only 14 subjects. Assume that we want to treat 14 healthy humans with this new drug and we have 16 suitable volunteers available.

a. If the subjects are selected and treated one at a time in sequence, how many different sequential arrangements are possible if 14 people are selected from the 16 that are available?

ZIP Code If you randomly select five digits, each between 0 and 9, with repetition allowed, what is the probability you will get the author’s ZIP code?

Computer Variable Names A common computer programming rule was that names of variables must be between one and eight characters long. The first character can be any of the 26 letters, while successive characters can be any of the 26 letters or any of the 10 digits. For example, allowable variable names include A, BBB, and M3477K. How many different variable names are possible? (Ignore the difference between uppercase and lowercase letters.)

High Fives

b. If n mathletes shake hands with each other exactly once, what is the total number of handshakes?