Chapter 15

How many different arrangements of the letters A, B, C, D, E, and F can be made? 720

Two dice are tossed. Find the probability of rolling each of the following events: \text { A sum of } 6 \frac{5}{36}

Two coins are tossed. Find the probabil- ity of tossing each of the following events: One head and one tail See below

If a woman has two skirts and ten blouses, how many different skirt-blouse combinations does she have? 20

In Problems \(1-12\), evaluate each.\(P(5,3)\)

How many different nine-letter arrangements can be formed from the nine letters of the word APPARATUS? \(\quad 30,240\)

If a man has eight shirts, five pairs of slacks, and three pairs of shoes, how many different shirt-slacks-shoe combinations does he have? 120

Find the probability of tossing each of the following events: Two tails

Evaluate each.\(P(8,2)\)

How many odd numbers of three different digits each can be formed by choosing from the digits \(1,2,3,5,7\), 8 , and 9 ? 150

In how many ways can four people be seated in a row of four seats?

Evaluate each.\(P(6,4)\)

In how many ways can Arlene, Brent, Carlos, Dave, Ernie, Frank, and Gladys be seated in a row of seven seats so that Arlene and Carlos are side by side? 1440

How many numbers of two different digits can be formed by choosing from the digits \(1,2,3,4,5,6\), and 7 ?

Find the probability of rolling each of the following events:A sum greater than 1 1

Evaluate each.\(P(9,3)\)

In how many ways can a committee of three people be chosen from six people? 20

How many even numbers of three different digits can be formed by choosing from the digits \(2,3,4,5,6,7,8\), and 9 ? 168

Find the probability of tossing each of the following events: Three heads \(\frac{1}{8}\)

Evaluate each.\(C(7,2)\)

How many committees consisting of three men and two women can be formed from seven men and six women?

How many odd numbers of four different digits can be formed by choosing from the digits \(1,2,3,4,5,6,7\), and \(8 ? \quad 840\)

Evaluate each.\(C(8,5)\)

How many different five-card hands consisting of all hearts can be formed from a deck of 52 playing cards?

Evaluate each.\(C(10,5)\)

Suppose that the students at a certain university are to be classified according to their college (College ofApplied Science, College of Arts and Sciences, College of Business, College of Education, College of Fine Arts, College of Health and Physical Education), sex (female, male), and year in school \((1,2,3,4\) ). How many categories are possible? 48

If no number contains repeated digits, how many numbers greater than 500 can be formed by choosing from the digits \(2,3,4,5\), and 6 ? 264

A medical researcher classifies subjects according to sex (female, male), smoking habits (smoker, nonsmoker), and weight (below average, average, above average). How many different combined classifications are used? 12

Evaluate each.\(C(12,4)\)

How many three-person committees can be formed from four men and five women so that each committee contains at least one man? 74

Four coins are tossed. Find the proba- bility of tossing each of the following events: Four heads \(\frac{1}{16}\)

A pollster classifies voters according to sex (female, male), party affiliation (Democrat, Republican, Independent), and family income (below \(\$ 10,000\), \(\$ 10,000-\$ 19,999, \$ 20,000-\$ 29,999, \$ 30,000-\$ 39,999\), \(\$ 40,000-\$ 49,999, \$ 50,000\) and above). How many combined classifications does the pollster use? 36

Find the probability of tossing each of the following events:Four heads \(\frac{1}{16}\)

Evaluate each.\(C(15,2)\)

How many different four-person committees can be formed from eight people if two particular people refuse to serve together on a committee? 55

A couple is planning to have four children. How many ways can this happen in terms of boy-girl classification? (For example, \(B B B G\) indicates that the first three children are boys and the last is a girl.) 16

Evaluate each.\(P(5,5)\)

How many four-element subsets containing A or \(B\) but not both \(A\) and \(B\) can be formed from the set \(\mid A, B, C\), \(\mathrm{D}, \mathrm{E}, \mathrm{F}, \mathrm{G}, \mathrm{H}] ? \quad 40\)

In how many ways can three officers - president, secretary, and treasurer - be selected from a club that has 20 members? 6840

Find the probability of getting each of the following events:At least one tail \(\frac{15}{16}\)

Evaluate each.\(C(5,5)\)

How many different six-letter permutations can be formed from four identical H's and two identical T's? 15

In how many ways can three officers - president, secretary, and treasurer - be selected from a club with 15 female and 10 male members so that the president is female and the secretary and treasurer are male?

Evaluate each.\(C(11,1)\)

How many four-person committees consisting of two seniors, one sophomore, and one junior can be formed from three seniors, four juniors, and five sophomores? 60

How many permutations of the four letters A, B, C. and \(D\) can be formed by using all the letters in each permutation? 24

A state has agreed to have its automobile license plates consist of two letters followed by four digits. State officials do not want to repeat any letters or digits in any license numbers. How many different license plates will be available? \(3,276,000\)

A disc jockey wants to play six songs once each in a halfhour program. How many different ways can he order these songs? 720

In how many ways can six students be seated in a row of six seats?

A state has agreed to have its automobile license plates consist of two letters followed by four digits. State officials do not want to repeat any letters or digits in any license numbers. How many different license plates will be available? \(\quad 3,276,000\)