Answer:
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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Be careful, I mixed in some problems that are not Permutation/Combination into the below set.
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?