# How many ways can the positions of president and vice president be assigned from a group of 8 people?

1) Solve for the factorials below: a) 4!

b) 0!

c) (3!)(2!)

d) 10!/8!

2) Evaluate each:

a) 9P9

b) 9C9

c) 9P5

d) 9C5

3) How many ways can you turn in a batting order for a baseball team if you only have 9 players?

4) Suppose a lawyer must select 4 jurors from a set of six candidates? How many groups are possible?

5) How many ways can 3 runners be selected for the Olympics from a field of 5 contestants?

6) How many ways can the first 3 places be awarded in a race involving  5 contestants (excluding ties)?

7) How many ways can the positions of president and vice president be assigned from a group of 8 people?

8) Find  the Number of hugs possible in a family of 5 people (no repeat hugs).

9) You have 9 families you would like to invite to a wedding. Unfortunately, you can only invite 6 families. How many different sets of invitations could you write?

10) Suppose we have to select 5 managers from a list of 10. How many ways can this be done? Give the correct expression that gives the answer.

11) Suppose we have to select a manager, assistant manager, and night manager from a list of 10 people. How many ways can this be done? Give the correct expression that gives the answer.

12) How many ways can a 3-card hand be selected from a standard 52-card deck? Give the correct expression that gives the answer.

13) Three cards are selected randomly and given to 3 players. How many possibilities exist? Give the correct expression that gives the answer.

14) A card is select from a standard deck of cards, then put back and the deck is shuffled. This is done 3 times. How many 3-card hands can you receive?

15) At a Fiat dealership a total of 3 cars of a particular model must be transported to another dealership. If there are 25 cars of this type, how many choices are available for transport?

16) At a Fiat dealership a total of 3 cars of a particular model must be transported to another dealership. If there are 25 cars of this type, how many ways can they be loaded onto the truck for transport?

17) At a Fiat dealership there are 25 cars of a certain model. Fifteen have automatic transmission. Twelve have leather seats. Ten cars have both automatic transmission and leather seats. a) How many have either automatic transmission or leather seats.

b) How many have neither automatic transmission nor leather seats.

18) Social Security numbers consist of 9 digits (0-9). If there are no restrictions, how many different social security numbers are possible?

19) Suppose license plates in one state have 4 letters followed by 2 digits. a) How many license plates can be created if there are no other restrictions?

b) What if only letters cannot be repeated?

c) What if only digits cannot be repeated?

20) A shipment of 20 disk drives were received by a computer store. Four of the drives are defective. A sample of 2 are selected randomly.

a) How many different samples can be selected?

b) How many of the samples contain 2 defective drives?

c) Suppose one of the samples is tested and one sample is sold. How many ways can this be done?

21) Suppose a 5-card hand is selected from a standard deck of cards. How many ways can the following be done? a) Select 3 Kings and 2 Aces

b) Select exactly 3 fours.

c) At least 4 hearts

22)  Suppose we have an office of 5 women and 6 men and need to select a 4 person committee. How many ways can we select a) 2 men and 2 women?

b) 3 men and 1 woman?

c) All women?

23) . A lottery consists of 54 numbers. To purchase a ticket, you select 6 numbers from 54 without repetition. How many selections are possible? (In lotteries, the order is generally not relevant.)

Just for fun, what if you had to get the numbers in the order selected?

24) Out of 30 applicants, 11 are female, 17 are college graduates, 7 are bilingual, 3 are female graduates, 2 are bilingual women, 6 are bilingual graduates and 2 are bilingual female graduates. Find the number of female graduates that are not bilingual.

25) a) How many 3 letter code words can be selected if there are no restrictions? b) How many 3 letter code words can be selected if repetition is not allowed?

26) Seven coins are tossed. How many different ways can they land?

27) There are 7 women and 5 men in a class. The instructor must select 5 to be on a committee. How many ways can the instructor select, a) a group of 3 women and 2 men?

b) a group of 2 women and 3 men?

c) a group of all women?

d) a group of all men?

Denise H.

In how many ways can a president and vice president be selected from a club consisting of 12 people? (Assume that theses 2 positions cannot be occupied by the same person)

## 2 Answers By Expert Tutors

president = A, vice president = B

president = B, vice president = A

are both acceptable, then what we have is a permutation question.

How many permutations are there of 12 men taken 2 at a time.

We use the formula for permutations of n things taken r at a time

! is the factorial symbol

Substituting 12 for n and 2 for r, we have

12! / 10! = 12 x 11 = 132

Imagine we have two slots representing the number of options for president and vice-president (respectively) out of our 12-person club:

For president, we have 12 possible options:

Once we've decided on a president, we now only have 11 possible people to choose from for vice-president:

Multiplying these options together gives us:

12*11 = 132 possible ways to choose President and Vice-President

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