1) Solve for the factorials below:
a) 4!
Show Answer
24
b) 0!
Show Answer
1
c) (3!)(2!)
Show Answer
12
d) 10!/8!
Show Answer
90
2) Evaluate each:
a) 9P9
Show Answer
9!=362,280
b) 9C9
Show Answer
1
c) 9P5
Show Answer
15,120
d) 9C5
Show Answer
126
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?
Show Answer
9P9=362,280
4) Suppose a lawyer must select 4 jurors from a set of six candidates? How many groups are possible?
Show Answer
6C4=60
5) How many ways can 3 runners be selected for the Olympics from a field of 5 contestants?
Show Answer
5C3=10
6) How many ways can the first 3 places be awarded in a race involving 5 contestants (excluding ties)?
Show Answer
5P3=60
7) How many ways can the positions of president and vice president be assigned from a group of 8 people?
Show Answer
8P2=56
8) Find the Number of hugs possible in a family of 5 people (no repeat hugs).
Show Answer
5C2=10
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
9C6=84
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
10C5
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
10P3
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
52C3
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
52P3
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
52*52*52=140,608
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
25C3=2300
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
25P3=13,800
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
17
b) How many have neither automatic transmission nor leather seats.
Show Answer
8
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
10*10*10*10*10*10*10*10*10=109 =1,000,000,000
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?
Show Answer
(264)(102)=45,687,600
b) What if only letters cannot be repeated?
Show Answer
26(25)(24)(23)(102)=35,880,000
c) What if only digits cannot be repeated?
Show Answer
(264)(10)(9)= 41,127,840
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
Combination Problem: 20C2=190
b) How many of the samples contain 2 defective drives?
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Combination Problem: 4C2=6
c) Suppose one of the samples is tested and one sample is sold. How many ways can this be done?
Show Answer
Permutation Problem: 20P2=380
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
Show Answer
(4C3)(4C2)=4(6)=24
b) Select exactly 3 fours.
Show Answer
(4C3)(48C2)=4(1128)=4512
c) At least 4 hearts
Show Answer
27885+1287=29,172
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
(5C2)(6C2)=150
b) 3 men and 1 woman?
Show Answer
(5C3)(6C1)=60
c) All women?
Show Answer
(5C0)(6C4)=15 or just 6C4=15
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
54C6=25,827,165
Just for fun, what if you had to get the numbers in the order selected?
Show Answer
54P6=18,595,558,800 (don't hold your breath)
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
1
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)
17,576
Answer b)
15,600
26) Seven coins are tossed. How many different ways can they land?
Show Answer
27 =128
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
350
b) a group of 2 women and 3 men?
Show Answer
210
c) a group of all women?
Show Answer
21
d) a group of all men?
Show Answer
1