Twenty one cancer patients volunteer for a clinical trial. Nine of the patients will receive a placebo and Twelve will receive the trial drug. In how many different ways can the researchers select 12 patients to receive the trial drug from the total of 21? Number of ways

Q: You and 19 of your friends have decided to form an Internet marketing consulting firm. The group…

A: There are a total of 20 people. So we need to choose a CEO, an operating manager, and a treasurer…

Q: In an office of 18 people, there are 7 men and 11 women. A subcommittee of four people will be…

A: Given: total = 18 members Number of men = 7 Number of female = 11

Q: A car dealership offers 10 different upgrades with each of the vehicles it sells. If a customer can…

A: Given data; A car dealership offers 10 different upgrades with each of the vehicles it sells.  To…

Q: The organizer of a conference is selecting workshops to include. She will select from 8 workshops…

A: We have given that  She will select from 8 workshops about music and 8 about poetry.

Q: Pizza House offers 2 different salads, 7 different kinds of pizza, and 4 different desserts. How…

A: Given :  Pizza House offers 2 different salads, 7 different kinds of pizza, and 4 different…

Q: Kara did a survey to determine to study the types of pets that students in her school had. She…

A:

Q: Motors Inc. manufactured 325 cars with automatic transmissions, 216 with power steering, and 89with…

A: We have given,

Q: A friend of mine is giving a dinner party. His current wine supply includes 11 bottles of zinfandel,…

A:

Q: An ice-skating rink inspects 25 pairs of skates and finds 2 pairs to be defective. rink has 150…

A: Given       an ice -skating rink inspects 25 pairs of skates…

Q: Of 10 possible books, you plan to take 4 with you on vacation. How many different collections of 4…

A:

Q: A dog shelter is giving away 16 different dogs, but you have room for only 4 of them.  How many…

A: Given, Number of different dogs given by shelter =16 There is exactly 1 room that can accommodates…

Q: There are 18 males and 14 females in a classroom. A president, secretary and vice- president must be…

A: There are 18 males and 14 females in a classroom. A president, secretary and vice president must be…

Q: How many different ways can the golf pro at a golf club select a foursome consisting of 1 man and 3…

A: Given,   Number of males = 8 Number of females = 11   The objective is to find how many different…

Q: The table d'hote (complete meal) at a french restaurant consists of a salad, enree, and a dessert.…

A: There are 2 salad choices, 5 entrée choices, and 3 dessert choices.

Q: A veterinarian surveys 26 of his patrons. He discovers that 14 have dogs, 10 have cats, and five…

A:

Q: A dog shelter is giving away 16 different dogs, but you have room for only six of them. How many…

A: A dog shelter is giving away 16 different dogs. And there is room for only six of them.

Q: A survey of 500 high school students was taken to determine their favorite chocolate candy. Of the…

A: we have to find given  probability

Q: From the 10 male and 12 female sales representatives for an insurance company, a team of 4 men and 2…

A:

Q: Out of 8800 kids visited a restaurant, 2400 like pizza, 3360 like burgers, and 2240 like sandwich,…

A: It is given that out of 8,800 kids 2,400 likes pizza, 3,360 like burgers and 2,240 likes sandwich.

Q: A baseball team is having a walk-on tryout camp for players. Thirty-four players show up at camp,…

A: Number of players (n) = 34 Coaches choosing only (r) = 3 By using combination formula

Q: Pizza House offers 2 different salads, 5 different kinds of pizza, and 3 different desserts. How…

A: From the provided information, Pizza house offers 2 different salads, 5 different kinds of pizza and…

Q: n soccer, a tie at the end of regulation time leads to a shootout by three members from each team.…

A: Given that  Number of players available (n) = 11 Players need to be selected = 3   We know that We…

Q: Pizza House offers 3 different salads, 7 different kinds of pizza, and 5 different desserts. How…

A: We have given that a Pizza house offers 3 different salads, 7 different kinds of pizza and 5…

Q: piggy bank contains 20 pennies, 4 nickels, 7 dimes, and 2 quarters. in how many ways can i select…

A: Given, piggy bank contains 20 pennies, 4 nickels, 7 dimes, and 2 quarters. We have to select only…

Q: The All-County Goat Show will award the blue ribbon for 1st place, red ribbon for 2nd place, and…

A: Using permutations and combination

Q: A company has 12 males and 9 female employees, and needs to nominate 2 men and 2 women for the…

A: Determine the number of teams can be formed.   The number of teams that can be formed is…

Q: A computer company has 5 vaccines in its executive trainee program. The company must select the…

A: Given - A computer company has 5 vaccines in its executive trainee program. The company must select…

Q: Two cards are chosen from a 52-card deck, how many ways can 2 Queens be choser

A: There are total of 4 queens in the deck of 52 cards.  We need to choose 2 queens .

Q: How many ways can a team of 28 hockey players choose a captain and two alternate captains?

A: Given that, There are 28 players in a hockey team.

Q: The manager of the winning soccer team chooses three of the 20 members to be interviewed by a sports…

A:

Q: In a class of 100 students, 42 students like Economics and 56 students like Art. 10 students don't…

A: Denote:  E: likes Economics A: Likes Arts AUE: Likes Economics or Arts A∪E: Likes Economics and Arts…

Q: A teacher chooses 3 of her 22 students to help clean the room after school. In how many ways can the…

A:

Q: A local radio station took a poll of 90 of its listeners to find out whether they like to watch…

A: let M be the listeners who like mariners games SE be the listeners who like seahawks games, SO be…

Q: A group of 12 service dogs have been trained as K-9 units to assist the SWAT unit. How many ways are…

A: This is a combinatorics problem. So number of ways to select 3 dogs from 12 is:  C12,3=12!3!12-3!…

Q: In a group of 50 patrons 18 patrons like lattes 16 patrons like espressos and 8 patrons like both…

A:

Q: How many different meals are possible from a menu if you choose one each of 5 appetizers, 4 entrées,…

A: Given data : Number of appetizers= 5 Number of entrees= 4 Number of desserts= 3 Number of beverages=…

Q: A college survey was taken to determine where students study. Of 140 students s cafeteria, 76…

A:

Q: The number of ways in which 2 cards can be chosen or selected from a total of 6 cards equals:

A: We are asked to find the number of ways of selecting 2 cards from 6 cards

Q: A restaurant offers a choice of 5 salads, 15 main courses, and 9 desserts. How many possible…

A: We have find the probability of given problem.

Q: A veterinarian surveys 28 of his patrons.  He discovers that 12 have dogs, 10 have cats, and 6 have…

A:

Q: A president, a treasurer, and a secretary are to be chosen from a committee with 44 members. In how…

A:

Q: A public health inspector wishes to inspect four restaurants by the end of the week. She has a list…

A: Given: Number of high-risk premises restaurants is 26, that is, x1=26. Number of medium-risk…

Q: You baked seven cupcakes of different flavor. In how many ways can you  give two cupcakes each to…

A: Here Given  Total No of cupcakes=7 No of given to each friends=2 No of cupcakes keep with himself=1

Q: There are 6 different types of fruits and n different types of vegetables in a grocery shop. If…

A: Introduction: According to the permutation rule, if r distinct items are to be chosen from n items…

Q: A contractor has three styles of homes, each with three styles of garages, two styles of decks, and…

A: Answer: First we need to list all the possible selections and the number of choices that each…

Q: A restaurant offers a choice of 4 salads, 13 main courses, and 6 desserts. How many possible…

A: Permutation and Combination: The different methods in which objects from a set could well be…

Q: If you pick 4 cards without replacement from a standard deck of 52 cards, how many different…

A:

Q: A sports store sells tennis racquets of six different prands: Wilson, Prince, Babolat, Dunlop, Yonex…

A: There are 6 brands we need to select 4 brands Out of the 4 brands Wilson or Prince should always be…

Q: rom the 7 male and 6 female sales representatives for an insurance​ company, a team of 4 men and 4…

A: It is given, Number of male representatives is 7, Number of female representatives is 6, A team of 8…