1) Solve for the factorials below: a) 4! Show Answer b) 0!Show Answer c) (3!)(2!)Show Answer d) 10!/8!Show Answer 2) Evaluate each:a) 9P9 Show Answer b) 9C9 Show Answer c) 9P5 Show Answer d) 9C5 Show Answer 3) How many ways can you turn in a batting order for a baseball team if you only have 9 players?Show Answer 4) Suppose a lawyer must select 4 jurors from a set of six candidates? How many groups are possible? Show Answer 5) How many ways can 3 runners be selected for the Olympics from a field of 5 contestants?Show Answer 6) How many ways can the first 3 places be awarded in a race involving 5 contestants (excluding ties)?Show Answer 7) How many ways can the positions of president and vice president be assigned from a group of 8 people?Show Answer 8) Find the Number of hugs possible in a family of 5 people (no repeat hugs).Show Answer 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? Show Answer 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.Show 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.Show 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.Show Answer 13) Three cards are selected randomly and given to 3 players. How many possibilities exist? Give the correct expression that gives the answer.Show 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?Show Answer 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?Show Answer 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?Show Answer 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.Show Answer b) How many have neither automatic transmission nor leather seats.Show Answer 18) Social Security numbers consist of 9 digits (0-9). If there are no restrictions, how many different social security numbers are possible?Show Answer Show Answer b) What if only letters cannot be repeated?Show Answer c) What if only digits cannot be repeated?Show Answer 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?Show Answer b) How many of the samples contain 2 defective drives?Show Answer c) Suppose one of the samples is tested and one sample is sold. How many ways can this be done?Show Answer 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 AcesShow Answer b) Select exactly 3 fours.Show Answer c) At least 4 heartsShow Answer 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?Show Answer b) 3 men and 1 woman?Show Answer c) All women?Show Answer 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.)Show Answer Just for fun, what if you had to get the numbers in the order selected? Show Answer 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.Show Answer 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?Show Answer 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?Show Answer b) a group of 2 women and 3 men?Show Answer c) a group of all women?Show Answer d) a group of all men?Show Answer 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 Recommended textbooks for you  College Algebra (MindTap Course List) Author:R. David Gustafson, Jeff Hughes Publisher:Cengage Learning College Algebra College Algebra Publisher:Cengage Learning Holt Mcdougal Larson Pre-algebra: Student Edition... Elementary Geometry For College Students, 7e Author:Alexander, Daniel C.; Koeberlein, Geralyn M. College Algebra Author:James Stewart, Lothar Redlin, Saleem Watson Publisher:Cengage Learning College Algebra (MindTap Course List) ISBN:9781305652231 Author:R. David Gustafson, Jeff Hughes Publisher:Cengage Learning College Algebra ISBN:9781938168383 Author:Jay Abramson Publisher:OpenStax College Algebra ISBN:9781337282291 Author:Ron Larson Publisher:Cengage Learning Holt Mcdougal Larson Pre-algebra: Student Edition... ISBN:9780547587776 Author:HOLT MCDOUGAL Publisher:HOLT MCDOUGAL Elementary Geometry For College Students, 7e ISBN:9781337614085 Author:Alexander, Daniel C.; Koeberlein, Geralyn M. Publisher:Cengage, College Algebra ISBN:9781305115545 Author:James Stewart, Lothar Redlin, Saleem Watson Publisher:Cengage Learning |
How many ways can the positions of president and vice president be assigned from a group of 8 people?
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