Probability and Counting Methods

Michael has 12 DVDs in a box:  8 comedies and 4 horror.  The probability of Michael reaching his hand into the box and randomly selecting 2 comedies can be written as....

• _{C(8,2) / C(12,2)}

• C(4,2) / C(8,4)

• C(8,2) / C(12,8)

• C(8,2) / C(4,2)

Jackie wants to select 4 of her 12 books to bring with her on vacation.  In how many ways can Jackie make her selection?

• 48

• 11880

• 495

• 24

Tricia wants to place her 10 DVDs on a shelf. How many arrangements are there for her DVDs?

• 100

• 3628800

• 1

• 10

One internet site requires you to create a password consisting of 2 letters followed by 4 digits.  The digits may not be repeated.  How many different passwords can be created?

• 6760000

• 3276000

• 92

• 3407040

One bank assigns each customer an 8 digit account number.  The number 0 can not be used as the first digit.  The last digit must be even.  How many account numbers can be created?

• 45000000

• 100000000

• 90000000

• 16777216

In a certain card game, only the number cards (from 2 - 10) are used.  Therefore, the entire deck of cards consists of only 36 cards.  Each player is dealt 6 cards.  How many different 6-card hands are possible, assuming the same 6 cards in different orders are counted as different hands?

• 216

• 2176782336

• 1402410240

• 1947792

4 children from the same family are all getting their hair cut by the same barber.  How many different arrangements are possible for the children to see the barber?

• 16

• 256

• 1

• 24

A seven-question quiz has 4 true/false questions followed by 3 multiple choice questions. For each multiple choice question there are four possible answers. In how many different ways is it possible to answer the seven questions?

• 12

• 80

• 28

• 1024

How many styles of sneakers are possible if Jared can choose from high-top or low-top, shoelaces or velcro, and the colors black, white, and red?

• 12

• 7

• 223

• 64

How many ways can a club select a president, vice president, and a secretary from a group of 5 people?

• 12

• 60

• 15