Permutations and Combinations Questions and Answers

A spinner has eight equal-sized sections labeled A, B, C, D, E, F, G, and H. What is the number of possible outcomes if you spin the spinner three times and the first spin is a vowel? 8 24 128 512

There are 25 students in your class. Your teacher wants to choose a group of 5. In how many ways can she form a group of 5 students? 5 25 53,130 6,375,600

You are playing a battle with your character cards. You brought 20 cards with you, but can only choose 5 for the battle. In how many ways can you choose the 5 cards? 1,860,480 20 5 15,504

A license plate begins with three letters chosen from A to Z. Which of the following represents the number of ways the letters of the license plate can be formed if you can repeat the letters? 26-3 26-26-26 326 26 +3

A license plate is to consist of 3 letters followed by 5 digits. Determine the number of different license plates possible if the first letter must be an K, L, M, N or P and repetition of letters and numbers is not permitted. 90,720,000 272,160,000 54,522,000 9,072,000

In how many possible ways can you arrange frults in a row out of a basket of two oranges, one apple, and four lemons? 105 630 5,040 823,543

Elizabeth rolls a number cube four times such that each roll represents a digit of a four-digit number. Which of the following expressions represents the number of four-digit numbers that are even that Elizabeth could obtain? 6x3 6 x 4 6x6x6x3 6x6x6x6

In how many possible ways can you arrange the digits in the order confirmation number 3018281268? 151,200 301,400 3,628,800 1,000,000

A certain lottery requires players to select 5 different numbers, in any order, from 1 to 48 inclusive. How many different sets of 5 numbers can be chosen? The 5 numbers can be chosen in different ways.

A ferris wheel is 50 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 6 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. What is the Amplitude? What is the Midline? y = What is the Period? How High are you off of the ground after 3 minutes?

Guests at a wedding have an appetizer choice of soup or a salad, an entrée choice of chicken, steak, or vegetarian, then a dessert choice of vanilla or chocolate cake. How many different meals are possible?

A woman has nine skirts and six blouses. Assuming that they all match, how many different skirt-and-blouse combinations can she wear? different skirt-and-blouse combinations. The woman can wear (Type a whole number.)

Determine whether the following are permutations or combinations The ways to form a three person committee of a chair, a treasurer, and a secretary from a group of eighteen people The ways to form a three 1. Permutations person committee from a group of eighteen people The ways to arrange the 2. Combinations letters Q, U, E, S, T, I, O, N The ways to get exactly three heads in ten tosses of a coin

The transaction history at an electronic goods store indicates that 21 percent of customers purchase the extended warranty when they buy an eligible item. Suppose customers who buy eligible items are chosen at random, one at a time, until one is found who purchased the extended warranty. Let the random variable P represent the number of customers it takes to find one who purchased the extended warranty. Assume customers' decisions on whether to purchase the extended warranty are independent. What is the probability that it takes more than 4 customers who buy an eligible item to find one who purchased the extended warranty?

Ms. Kelly's daughter has 8 stuffed animals that she absolutely loves. a) She is allowed to bring one stuffed animal to school each day for three days in a row. In how many ways can choose to bring her toys? b) She is lining her toys up for a picture, in how many ways can she line up all her toys? c) She is playing "princess" and is using three of her toys as characters. In how many ways can she assign the roles, King, Queen, and Knight? d)While going on vacation she is allowed to bring three stuffed animals with her. In how many ways can she select the toys to bring?

Four starting youth basketball players are ages 8, 10, 9, and 11. Solve for the number of samples if a sample of two is randomly chosen. Show your work and explain the steps you used to solve.

a. How many teams of six can be chosen out of 54 people? i. What type of problem? ii. Solve b. Out of 54 people how many ways are there to nominate a President and Vice President for the group i. What type of problem? ii.Solve

4. Identify which of the following is a permutation question a. If there are 120 students in grade 11, how many ways can a seating chart be made for a group of 18 of the students? b. If there are eight classrooms on a school floor and twenty desks in each classroom, how many desks are there to choose from to sit in? c. How many groups of 10 students can be selected out of a class of 32 students?

In both videos, Sal uses the mathematical operation factorial. Evaluate the following factorial expressions, and watch this video if you need help. Note: the answers to (a) and (b) are different!

A lottery system uses six digits. The possible entries in these digits are the numbers 1, 2, 3, 4, or letters n, m, o, q, s, w, and z. The numbers or letters drawn can be repeated. What is the total number of lottery sequences that can be made? 823,543 1,771,561 1,000,000 121,745

A football player attempts a total of 8 passes in overtime. Each pass can result in one of 3 possible outcomes (a completion, an incompletion, or a turnover). How many ways could they complete the 8 passes?

Diltiazem is a commonly prescribed drug for hypertension. However, diltiazem causes headaches in about 12% of patients using the drug. It is thought that regular exercise might help reduce the headaches. If a random sample of 209 patients using diltiazem exercised regularly and only 16 had headaches, would this indicate a reduction in the population proportion of patients having headaches? Use a 1% level of significance.

Over the weekend, your family is going on vacation. Your mom is letting you bring 5 DVDs for the long road trip. How many ways can you choose the five DVDs if you have 12 DVDs in all? (order does not matter) 1012 60 512 792

Pepperoni, green olives, black olives, tomatoes, green peppers, bacon, and hamburger are topping selections for a pizza. How many 2-topping possibilities are there, in which the toppings are not used more than once? 21 49 36 64

Outside a home, there is a 6-key keypad with letters A, B, C, D, E and F that can be used to open the garage if the correct six-letter code is entered. Each key may be used only once. How many codes are possible? The number of possible codes is

How many different arrangements of 4 letters can be formed if the first letter must be W or K (repeats of letters are allowed)? There are different 4-letter combinations that can be formed. (Simplify your answer.)

License plates in a particular state display 2 letters followed by 2 numbers. How many different license plates can be manufactured for this state? There are different license plates that can be manufactured for this state.

A spinner is divided into 15 identical sectors and labeled 1 through 15. How many spins are expected for a multiple of 4 to be spun 7 times? Select from the drop-down menu to correctly complete the sentence. The spinner is expected to have to spin approximately Choose... times for a multiple of 4 to be spun 7 times.

Find the equation of a 3D figure matching each of the descriptions below: a. A set of points equidistant from the origin. b. A plane parallel to the xy-plane. c. A plane parallel to the yz-plane. d. A plane parallel to the xz-plane. e. A point on the x-axis in 3D space. f. A point on the y-axis in 3D space. g. A point on the z-axis in 3D space. h. A plane centered at the origin with normal vector < 2, 3, -4 >

Use the formula for nPr, to evaluate the following expression. 9P6

A medical researcher needs 6 people to test the effectiveness of an experimental drug. If 13 people have volunteered for the test, in how many ways can 6 people be selected?

Fill in the blank so that the resulting statement is true. If you can choose one item from a group of M items and a second item from a group of N items, then the total number of two-item choices is If you can choose one item from a group of M items and a second item from a group of N items, then the total number of two-item choices is

Ed must select and answer in any order four of twelve essay questions on a test. In how many ways can he do so? Enter your result in the space provided using number keys only.

Robin is single. Her taxable income is $71,511. Find the tax liability using the Tax Table, Exhibit 18-3 from your text. $8,200.32 $10,280.42 $11,671.92 $15,732.42

If a first experiment can be performed in 5 distinct ways and a second experiment can be performed in 8 distinct ways, the two experiments together can be performed in how many distinct ways? Enter your result in the space provided using number keys only.

Freight Train Cars In a train yard there are 7 tank cars, 12 boxcars, and 12 flatcars. How many ways can a train be made up consisting of 4 tank cars, 5 boxcars, and 5 flatcars? (In this case, order is not important.) Total number of ways =

For a segment of a radio show, a disc jockey can play 5 records. If there are 9 records to select from, in how many ways can the program for this segment be arranged?

A nursing student can be assigned to one of six different floors each day depending on staffing needs. How many different ways can she be assigned during a 4- day work week?

Kristen's financial advisor has given her a list of 13 potential investments and has asked her to select and rank her favorite four. In how many different ways can she do this?

A new computer graphics company employs 10 programmers. The company decides to expand into digital animation and needs to transfer 3 of the programmers into the new department. How many different combinations of 3 programmers can be chosen to transfer to the new department

When Bill makes a sandwich, he may choose from among 3 kinds of rolls, 4 varieties of meat, and 2 types of sliced cheese. If he chooses one roll, one meat, and one type of cheese, how many different kinds of sandwiches can he make? (A) 9 (B) 14 (C) 24 3x-420 (D) 288

A group of Mathematics faculty at the local college consists of 9 women and 9 men. Five people are to be selected to go to a conference. How many different ways can a group of five people be selected from this group of 18? In how many ways can five women be chosen from the group of 9 women? What is the probability that all women will be chosen to attend the conference? Enter a reduced fraction or decimal.

Peter wants to buy a sandwich. He can make his sandwich with sourdough, Italian, or whole wheat bread. He can choose turkey, ham, or salami. Each sandwich comes with either Provolone or American cheese. In how many possible ways can Peter make his sandwich if he chooses one item from each group? 6 8 9 18

A box of chocolates contains six milk chocolates and seven dark chocolates. You randomly pick a chocolate and eat it. Then you randomly pick another piece. What is the probability that the first piece is milk chocolate and the second is dark chocolate?

7. How many different 4-letter "words" can be made from the letters j, o, u, r, n, e, y if a. The first letter must be a vowel and repetitions are allowed? Show the computation used to arrive at your answer. b. The first letter must be an y, the last letter must be an r, and repetitions are not allowed? Show the computation used to arrive at your answer.

A race has 21 participants. How many ways can first second, and third place be decided assuming there is no tie?

Rita have a decorative M&M's dispenser in her house. When a guest activates the dispenser, this person gets a randomly selected M&M out of the container. The container has 10 Red M&M's, 8 Blue M&M's and 13 yellow M&M's.

The lines L₁, L2, L3,... L2₂0 are distinct. All the lines L4, L8, L12, L16 and L20 are parallel. All the lines L₁,L5, L9, L13, L17 pass through a given point A. The maximum number of points of intersection of these 20 lines is

A baseball player comes up to bat 3 times during a league game. He either gets a hit or gets an out. How many different combinations are there for the three at bats? Make a tree diagram to help see the situation. 8 different combinations 7 different combinations 6 different combinations 5 different combinations

In a state's Pick 3 lottery game, you pay $1.48 to select a sequence of three digits (from 0 to 9), such as 600. If you select the same sequence of three digits that are drawn, you win and collect $354.12. Complete parts (a) through (e). a. How many different selections are possible?