# 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!

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b) 0!

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c) (3!)(2!)

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d) 10!/8!

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2) Evaluate each:

a) 9P9

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b) 9C9

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c) 9P5

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d) 9C5

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

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

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

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

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

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

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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?

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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.

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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.

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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.

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

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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?

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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?

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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?

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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.

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

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

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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?

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b) What if only letters cannot be repeated?

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c) What if only digits cannot be repeated?

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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?

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

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

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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

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b) Select exactly 3 fours.

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c) At least 4 hearts

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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?

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b) 3 men and 1 woman?

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c) All women?

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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.)

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

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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.

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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?

Answer a)

Answer b)

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

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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?

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b) a group of 2 women and 3 men?

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c) a group of all women?

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d) a group of all men?

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Denise H.

asked • 09/15/14

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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