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mathematics
survey of mathematics
Questions and Answers of
Survey of Mathematics
In how many ways can the digits in the number 4,568,865 be arranged?
In how many ways can the letters in the word “MANAGEMENT” be arranged?
In how many ways can the letters in the word “STATISTICS” be arranged?
Determine the number of permutations of the letters of the word “SUCCESS.”
Determine the number of permutations of the letters of the word “EDUCATION.”
Keri is taking a 12-question multiple-choice exam. Each question has three possible answers, (a), (b), and (c). In how many possible ways can Keri answer the questions?
A disc jockey (DJ) has 9 songs to play. Five are slow songs, and 4 are fast songs. Each song is to be played only once. In how many ways can the DJ play the 9 songs if(a) The songs can be played in
A swimming event has fifteen participants. The 4 swimmers with the fastest speeds will be listed, in order, on the leader board. How many different ways are there for the names to be listed?
A teacher has 20 students and she will select 5 students to receive a prize. If each prize is different, in how many ways can the prizes be awarded to the students?
Twelve students are competing for 3 different writing scholarships. In how many ways can the scholarships be awarded?
Five different colored flags will be placed on a pole, one beneath another. The arrangement of the colors indicates the message. How many messages are possible if five flags are to be selected from
A skiing event has 16 participants for the slalom. The 5 participants with the fastest speeds will be listed, in the order of their speed, on the leader board. How many different ways are there for
There are 10 candidates for three positions at Johnny Rockets. One position is for a cook. The second position is for a food server. The third position is for a cashier. If all 10 candidates are
The trifecta at most racetracks consists of selecting the first-, second-, and third-place finishers in a particular race in their proper order. If there are seven entries in the trifecta race, how
If a club consists of 10 members, how many different arrangements of president, vice president, and secretary are possible?
Determine the number of permutations of the arrangement of colors in the spectrum that follows. Red Blue Violet Indigo
In one question on a history test, a student is asked to match 10 dates with 10 events; each date can be matched with only 1 event. In how many different ways can this question be answered?
A telephone number consists of seven digits with the restriction that the first digit cannot be 0 or 1. Repetition of digits is permitted.(a) How many distinct telephone numbers are possible?(b) How
A license plate is to consist of three digits followed by two uppercase letters. Determine the number of different license plates possible if. (a) Repetition of numbers and letters is
An identification code is to consist of three upper case letters followed by four digits. How many different codes are possible if (a) Repetition of letters and numbers is not permitted?(b)
At the reception line of a wedding, the bride, the groom, the best man, the maid of honor, the four ushers, and the four bridesmaids must line up to receive the guests.(a) If these individuals can
The six pictures shown are to be placed side by side along a wall.In how many ways can they be arranged from left to right if.(a) They can be arranged in any order? (b) The bird must be on the
Consider the five figures shown. In how many different ways can the figures be arranged (a) From left to right? (b) From top to bottom if placed one under the other? (c) From left
In Italy, most car and motorcycle license plates consist of 2 upper case letters, followed by 3 digits, followed by 2 upper case letters. (See photo.) Determine the number of license plates possible
A social security number consists of nine digits. How many different social security numbers are possible if repetition of digits is permitted?
Some doors on cars can be opened by pressing a correct sequence of buttons. A display of the five buttons by the door handle of a car follows.On most cars, although each key lists two numbers, the
Assume that a password to log onto a computer account is to consist of any four digits or letters (repetition is permitted). Determine the number of passwords possible if (a) The letters are not
The Johnsons just moved into their new home and are selecting furniture for the family room. They are considering 5 different sofas, 2 different chairs, and 6 different tables. They plan to select
At a computer store, a customer is considering 5 different computers, 4 different monitors, 7 different printers, and 2 different scanners. Assuming that each of the components is compatible with one
Kai plans to enroll in four classes: sociology, chemistry, economics, and humanities. There are seven sociology classes, four chemistry classes, three economics classes, and four humanities classes
Juan has three ties, four shirts, and two pairs of pants. How many different outfits can he wear if he chooses one tie, one shirt, and one pair of pants for each outfit?
There are four different routes that Cassidy can walk from home to the post office and two different routes that she can walk from the post office to the bank. How many different routes can Cassidy
To use an automated teller machine, you generally must enter a four-digit code, using the digits 0–9. How many four-digit codes are possible if repetition of digits is permitted?
Evaluate the expression.10P6
Evaluate the expression.8P4
Evaluate the expression.3P3
Evaluate the expression. 9P5
Evaluate the expression.6P0
Evaluate the expression.8P0
Evaluate the expression.4P3
Evaluate the expression.2P5
Evaluate the expression.1!
Evaluate the expression. 0!
Evaluate the expression.7!
Evaluate the expression.4!
Fill in the blank with an appropriate word, phrase, or symbol(s).The notation used to express the number of permutations of seven items taken two at a time is _________ .
Fill in the blank with an appropriate word, phrase, or symbol(s).The notation used to express the number of permutations of five items taken three at a time is __________ .
Fill in the blank with an appropriate word, phrase, or symbol(s).The number of permutations of no bjects, where n1 of the items are identical, n2 of the items are identical, . . . . , nr are
Fill in the blank with an appropriate word, phrase, or symbol(s).The formula for the number of permutations when r objects are selected from n objects is nPr = _________.
Fill in the blank with an appropriate word, phrase, or symbol(s).The formula for the number of permutations of n distinct items is n! = ___________.
Fill in the blank with an appropriate word, phrase, or symbol(s).The symbol for n factorial is ____________ .
Fill in the blank with an appropriate word, phrase, or symbol(s).To determine the number of distinct ways two or more experiments can be performed, the _________ principle can be used.
Fill in the blank with an appropriate word, phrase, or symbol(s).Any ordered arrangement of a given set of objects is called a(n) ___________ .
Fill in the blank with an appropriate word, phrase, or symbol(s).If n (E1 and E2) = 4 and n(E1) = 16, then P(E2|E1) = ______________.
Fill in the blank with an appropriate word, phrase, or symbol(s).If n (E1 and E2) = 3 and n(E1) = 7, then P(E2|E1) = ______________.
Fill in the blank with an appropriate word, phrase, or symbol(s).The notation for the probability of E2, given E1, is ___________.
Fill in the blank with an appropriate word, phrase, or symbol(s).The probability of event E2 occurring, given that event E1 has happened, is called a(n) ___________ probability.
Refer to the Recreational Math. Determine(a) The number of possible arrangements of the letters given.(b) The word when the letters are placed in the proper order.STEABK
Refer to the Recreational Math. Determine(a) The number of possible arrangements of the letters given.(b) The word when the letters are placed in the proper order.ROTES
An experiment consists of 3 parts: flipping a coin, tossing a rock, and rolling a die. If the sample space consists of 60 sample points, determine the number of faces on the rock.
All my ties are red except two. All my ties are blue except two. All my ties are brown except two. How many ties do I have?
A thumbtack is dropped on a concrete floor. Assume that the thumbtack can land only point up (u) or point down (d), as shown in the figure below. If two thumbtacks are dropped, one after the
Suppose that a bag contains one white chip and two red chips. Two chips are going to be selected at random from the bag with replacement. (a) What is the probability of selecting a white chip
A pea plant must have exactly one of each of the following pairs of traits: short (s) or tall (t); round (r) or wrinkled (w) seeds; yellow (y) or green (g) peas; and white (wh) or purple (p) flowers
An individual can be classified as male or female with red, brown, black, or blond hair and with brown, blue, or green eyes. (a) How many different classifications are possible (for ex-ample,
You decide to take a literature course. A requirement for the course is that you must read one classic book, one nonfiction book, and one science fiction book from the list below.If the books are
Mr. and Mrs. Frank just moved into a new home and need to do some landscaping. They are going to purchase one tree, one shrub, and one lilac bush at random from the list below.(a) Determine the
You visit Best Buy to purchase a new home theater system. You are going to purchase a Blu-ray player, a receiver, and a speaker system at random from among the following brands.(a) Determine the
You decide to take a science course, an English course, and a mathematics course during the next term. The available courses that you can take are listed below.If the courses are selected at
Three different people are to be selected at random, and each will be given one gift card. There is one card from Home Depot, one from Best Buy, and one from Red Lobster. The first person selected
From the list below, Steve will purchase one appetizer, one beverage, and one dessert at random to bring to a party.(a) Determine the number of sample points in the sample space. (b) Construct a
At a homeowners’ association meeting, a board member can vote yes, vote no, or abstain on a motion. There are three motions on which a board member must vote.(a) Determine the number of sample
A single fair die is rolled twice. (a) Determine the number of sample points in the sample space. (b) Construct a tree diagram and list the sample space. Determine the probability
Selby Gardens sells bonsai trees. Customers can choose a juniper, maple, fir, or boxwood bonsai tree. Customers can also choose a circular, oval, or square base in which to plant the tree. The Chens
The Flotterons plan to purchase paint for the walls and paint for the trim in their living room. They will select one color for the walls and one color for the trim at random from the following
Three coins are tossed. (a) Determine the number of sample points in the sample space. (b) Construct a tree diagram and list the sample space. Determine the probability that(c) No
A hat contains four marbles: 1 yellow, 1 red, 1 blue, and 1 green. Two marbles are to be selected at random without replacement from the hat.(a) Determine the number of sample points in the sample
A box contains three cards. On one card there is a sun, on another card there is a question mark, and on the third card there is an apple.Two cards are to be selected at random without
A box contains three cards. On one card there is a sun, on another card there is a question mark, and on the third card there is an apple.Two cards are to be selected at random with replacement.(a)
A couple plans to have two children. (a) Determine the number of sample points in the sample space of the possible arrangements of boys and girls. (b) Construct a tree diagram and list the
Two coins are tossed.(a) Determine the number of sample points in the sample space. (b) Construct a tree diagram and list the sample space. Determine the probability that(c) No tails are
Your television remote control has buttons for digits 0–9. If you press two buttons, how many numbers are possible if (a) The same button may be pressed twice. (b) The same button may not
A bag contains five batteries, all the same size and equally likely to be selected. Each battery is a different brand. If you select three batteries at random, use the counting principle to determine
If two dates are selected at random from the 365 days of the year, use the counting principle to determine the number of possible outcomes if the dates are selected(a) With replacement. (b)
If two lower case letters are selected at random from the English alphabet, use the counting principle to determine the number of possible outcomes if the letters are selected(a) With
Fill in the blank with an appropriate word, phrase, or symbol(s).A helpful method to determine a sample space is to construct a(n) ___________ diagram.
Fill in the blank with an appropriate word, phrase, or symbol(s).If a first experiment can be performed in three distinct ways and a second experiment can be performed in eight distinct ways, the two
Fill in the blank with an appropriate word, phrase, or symbol(s).Each individual outcome in a sample space is called a sample ___________ .
Fill in the blank with an appropriate word, phrase, or symbol(s).A list of all possible outcomes of an experiment is called a(n) ________ space.
The probability that a person is accepted for admission to a specific university is 0.6. Determine the probability that exactly two of the next five people who apply to that university get accepted.
A bin contains a total of 20 batteries, of which 6 are defective. If you select 2 batteries at random, without replacement, determine the prob-ability that (a) Both of batteries are
Three of six people are to be selected and given small prizes. One will be given a book, one will be given a calculator, and one will be given an iTunes card. In how many different ways can these
The number of cars and the number of SUVs going through the toll gates of the George Washington Bridge and the Golden Gate Bridge is recorded. The results are shown below.If one of these vehicles
You get to select one card at random from a standard deck of 52 cards. If you pick a club, you win $8. If you pick a heart, you win $4. If you pick any other suit, you lose $6. Determine your
A litter of collie puppies consists of four males and five females. If one of the puppies is selected at random, determine the odds.(a) Against the puppy being male.(b) In favor of the puppy being
A personal password for an Internet broker-age account is to consist of an uppercase letter, followed by two digits, followed by two uppercase letters. Deter-mine the number of personal codes
A chip other than a red chip or an even number.One colored chip—red, blue, or green—is selected at random and a fair die is rolled.By observing the sample space of the chips and die mentioned
A red chip or the number 1.One colored chip—red, blue, or green—is selected at random and a fair die is rolled.By observing the sample space of the chips and die mentioned above, determine the
A green chip and the number 2.By observing the sample space of the chips and die mentioned above, determine the probability of obtaining.
Construct a tree diagram illustrating all the possible out-comes and list the sample space.One colored chip—red, blue, or green—is selected at random and a fair die is rolled.
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