MATH 100 Ch. 10

How many ways can a president and vice-president be chosen from a committee of 11 people?

110

Assuming all members of the club are​ eligible, but that no one can hold more than one​ office, list and count the different ways the club could elect a president and a treasurer if the two officers must not be the same gender. N={Adam, Brian, Carla, Douglas, Emma} ​or, in abbreviated​ form, N={A, B, C, D, E}.

12 - AC, AE, BC, BE, CA, CB, CD, DC, DE, EA, EB, ED

Pamela​ DeMar's computer printer allows for optional settings with a panel of five on-off switches in a row. How many different settings can she select if no two adjacent switches can both be​ on?

13

How many ways can a teacher give four different prizes to four of her 22 ​students?

175560

You roll two six-sided dice, counting the sum of the results of each pair. Of the 36 possible outcomes, determine the number for which the sum of both dice is 3

2

How many ways can a male and a female be selected to decorate for a party from a club consisting of nine members where four are men and five are​ women?

20

A club N with five members is shown below. N={Alvin, Blake, Carrie, Daniel, Eileen}​, abbreviated as N={A, B, C, D, E} Assuming all members of the club are​ eligible, but that no one can hold more than one​ office, list and count the different ways the club could elect both a president and a treasurer.

20 - AB, AC, AD, AE, BA, BC, BD, BE, CA, CB, CD, CE, DA, DB, DC, DE, EA, EB, EC, ED

An electronics store receives a shipment of 30 graphing​ calculators, including 2 that are defective. Four of the calculators are selected to be sent to a local high school. How many of these selections will contain no defective​ calculators?

20475

When two fair dice are​ rolled, there are 36 possible outcomes. How many possible outcomes would there be if three fair dice were​ rolled?

216

Find the number of distinguishable arrangements of the letters of the word: HEEBIE−JEEBIES

2162160

In how many ways could 17 people be divided into five groups​ containing, respectively, 4​, 1​, 7​, 3​, and 2 people?

245044800

Of the 36 possible outcomes, determine the number for which the sum of both dice is greater than 5

26

Find the number of distinguishable arrangements of the letters of the word: DUODECILLION

29937600

Subject identification numbers in a certain scientific research project consist of two letters followed by three digits and then two more letters. Assume repetitions are not allowed within any of the three​ groups, but letters in the first group of two may occur also in the last group of two. How many distinct identification numbers are​ possible?

304200000

​Pamela's computer printer allows for optional settings with a panel of five ​on-off switches in a row. How many different settings can she select if there are no restrictions on the switches?

32

A contractor builds homes of 11 different models and presently has 6 lots to build on. In how many different ways can he arrange homes on these​ lots?Assume 6 different models will be built.

332640

List and count the ways club N could appoint a committee of three members when there are no restrictions to select the committee. N={Alan, Bill, Cathy, David } ​or, in abbreviated​ form, N = {A, B, C, D}

4 - ABC, ABD, ACD, BCD

In how many ways could members of the following club line up all 8 members for a​ photograph? N=​{Jim, Ashley, Emma, Anthony, David, Evelyn, Linda, Craig​}

40320

Jessica​ Elbern's class schedule for next semester must consist of exactly one class from each of the four categories shown in the table at the top of the next column. Use the table to determine the number of different sets of classes Jessica can take if funding has been withdrawn for two of the education courses and for one of the sociology courses.

48

The daily double at most race tracks consists of selecting the winning horse in both the first and second races. If the first race has 6 entries and the second race has 8 entries, how many daily double tickets must be purchased to guarantee a​ win?

48

Counting numbers are to be formed using only the digits 9, 5, 6, 7, 3, 8, and 4. Determine the number of different possibilities for​ two-digit numbers

49

An unusual die has the numbers 1​, 1​, 3​, 3​, 7​, and 7 on its six faces. Two of these dice are​ rolled, and the two numbers on the top faces are added. How many different sums are​ possible?

6

Counting numbers are to be formed using only the digits 4​, 5​, and 7. Determine the number of different possibilities for four-digit numbers with one pair of adjacent 5s and no other repeated digits​

6

How many of the anagrams​ (arrangements of the​ letters) of JNDJCNC are​ palindromes, that is arrangements that read the same forward and​ backward?

6

Assuming all members are​ eligible, but no one can hold more than one​ office, list and count the different ways the club could elect a​ president, a​ secretary, and a treasurer if the president must be a man and the other two must be women. ​(Carla and Eileen are​ women, and the others are​ men.) N={Alfred, Brad, Carla, Douglas, Eileen} ​or, in abbreviated​ form, N = {A, B, C, D, E}

6 - ACE, AEC, BCE, BEC, DCE, DEC

In a race in which ten automobiles are entered and there are no​ ties, in how many ways can the first three finishers come​ in?

720

Until​ 1995, the rules for​ three-digit area codes in the United States were as​ follows: •The first digit could not be 0 or 1. •The second digit had to be 0 or 1. •The third digit had no such restrictions. In​ 1995, the restriction on the second digit of area codes was removed. How many area codes are possible after the restriction is​ removed?

800

To win at LOTTO in one​ state, one must correctly select 6 numbers from a collection of 65 numbers​ (1 through 65​). The order in which the selection is made does not matter. How many different selections are​ possible?

82598880

For​ $3.98 you can get a​ salad, main​ course, and dessert at the cafeteria. If you have a choice of 4 different​ salads, 6 different main​ courses, and 4 different​ desserts, then how many different meals can you get for​ $3.98?

96

Construct a tree diagram showing all possible results when three fair coins are tossed. Then list the ways of getting fewer than two heads

TTT, HTT, THT, TTH

Determine whether the object is a permutation or a combination: the batting order for a baseball team

This is a permutation because repetition is not allowed and the order of the items matters.

Determine whether the object is a permutation or a combination: an automobile license plate number

This is neither a permutation nor a combination because reputation is allowed.

Determine whether the object is a permutation or a combination: a​ 10-digit telephone number​ (including area​ code)

This is neither a permutation nor a combination because reputation is allowed.

At a wedding​ reception, the bride and groom and seven attendants will form a receiving line. How many ways can they be arranged in each of following​ cases? ​a) Any order will do. ​b) The bride and groom must be the last two in line. ​c) The groom must be last in line with the bride next to him.

a) 362880 b) 10080 c) 5040