A horse race has 12 horses. i ) How many dierent ways can the podium be arranged? (The podium has a spot for only the 1st, 2nd and 3rd place horse) ii ) How many different ways can the horses finish the race such that Grand Valor, Seabiscuit and Secretariat do not finish first? iii ) How many dierent ways can the horses nish the race such that one horse (Grand Valor) always beats both Seabiscuit and Secretariat?

Q: Alice, Bob, Carl, and Diane are going to be coaches for a children's bas- ketball tournament. There…

A: Given: Number of coaches=4, total number of children's=20 and each team consist of 5 players.

Q: Five couples want to have their pictures taken. In how many ways can they arrange themselves in a…

A: Here we have to find the total numbers of ways so that they can arrange themselves in a row of…

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

A:

Q: In a music club with 16 members, 5 people played the piano, 11 played the guitar, and 3 didn’t play…

A: let A= set of  people in the club who played pianoB= set of people in the club who played…

Q: A bakery has 7 different kinds of donuts (chocolate, boston cream, sprinkle, old fashion, 2. honey…

A: Given: Number of donuts to be purchased by Cindy = 30 Different kinds of donuts = 7

Q: c) There are 5 airplanes ready to depart. Runway A and runway D are available. How Many ways can 2…

A: We Know that there are 5 airplanes ready to depart. Runway A and runway D are available. We have to…

Q: 7) From a club of 21 people, in how many ways can a group of four members be selected? 8) A…

A: According to the question-answer guidelines the expert suppose to answer only three sub parts.

Q: 2. Five boys and four girls are waiting for the MRT to arrive at Guadalupe Station. In how many ways…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: 20. The ski club with ten members is to choose three officers: captain, co-captain, and secretary.…

A: There are 10 members in the ski club. Three officers are to be chosen. Captain, co-captain, and…

Q: In a bag containing 5 white balls and 6 black balls, how many ways can we draw a white or a black…

A:

Q: From a list of 40 teachers, 5 are to be promoted to subject area coordinator. In how many ways can…

A: Given: n=40 and r=5.

Q: In the Pinoy Big Brother House, the original housemates composed of 6 males and 6 females were asked…

A: Here we solve the given problem.

Q: At a corporate dinner, five people including the president and vice president are sitting around a…

A: a) If 5 people sit on a circular table then the number of permutations will be 4!=24 b) If President…

Q: There are 5 bus lines from city A to B and 4 bus lines from city B to city C. Find the number of…

A:

Q: The BMCC math club has 50 members. a. In how many different ways can it select a group of 4…

A: he BMCC math club has 50 members.

Q: Seven women and nine men are on the faculty in the mathematics department at a school.   1. How…

A:

Q: 4. An expedition team consisting of 10 members to be chosen from a group of 4 teachers and 12…

A:

Q: A company has 10 male and 11 female employees, and needs to nominate 2 men and 2 women for the…

A: They can choose 2 men from 10 men in 10C2 ways They can choose 2 women from 11 women in 11C2 ways.…

Q: box with a square base and no top is to be made from a square piece of tin by cutting out a 3-inch…

A: Given, Square base No top Volume= 48 cubic inches

Q: The new license plates consists of three alphabet letters followed by three digits.  How many…

A: Given: A license plate consists of three alphabet followed by three digits. The objective is to…

Q: reen plates, 7 white plates ans 9 blue plates. In how many ways can a person make a selection of…

A:

Q: In a certain state, all car license plates have four capital letters followed by three digits.…

A:

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: A Convener and a Secretary are to be chosen from group of people consisting of 50 people. Explain…

A: i) We can select A as Convener in only 1 way. We can select Secretary from (50-1)=49 people in 49…

Q: 6. Number of ways a person can travel from A to C via B, if there are 3 routes from A to B and 5…

A: Let there are 3 places A, B and C. And given that there are 3 routes from A to B. And 5 routes from…

Q: A restaurant offers 4 appetizers and 6 main courses. In how many ways can a person order a​…

A: One object from m objects can be selected in mP1 ways.

Q: How many ways are there to go from B to D?

A: here given  A boy lives at B and wants to go to school at D. From his home B he has to first reach C…

Q: The board of directors of a corporation must select a president, a secretary, and a treasurer. In…

A: Given that there are total 14 members.    A president, a secretary, and a treasurer represent 3…

Q: There are twohighways from city A to city​ B, three highways from city B to city​ C, and two…

A: The solution is given below:

Q: In how many ways can 4 CS students and 5 IT students sit in a row if the CS and IT students must…

A:

Q: How many ways are there to stack an ice-cream cone with 4 scoops if the choices are a. cookie dough,…

A: To calculate the total number of ways to take an ice-cream cone with 4 scoops if the choices are…

Q: At the first tri-city meeting, there were 5 people from town A, 4 people from town B, and 2 people…

A:

Q: the chairperson who must select a subcommittee but assume that the committee consists of 11 people…

A: There are total 11 people including the chairperson. 1 chairperson is to be selected at first. The…

Q: A builder is planning to build 12 houses along one side of a road. He will build 2 houses in style…

A: Given data: The total numbers of houses are n=12. The number of styles A house is A=2. The number of…

Q: A college has 3 entrance gates and 2 exit gates. In how many ways can a student enter then leave the…

A:

Q: A mother of 8 wanted to attend a party but only 5 children can be fit in her car. In how many ways…

A:

Q: Five couples want to have their pictures taken. In how many ways can they arrange themselves in a…

A: Given: Five couples want to have their pictures taken. In how many ways can they arrange themselves…

Q: How many ways are there for three men and six women to stand in a line (a) so that all women stand…

A: In first case club all women together. Then the problem becomes number of ways in which 3 men and 1…

Q: Four married couples have reserved eight seats in a row at the   theater, starting at an aisle seat.…

A: As given above there are four married couples have reserved eight seats in a row. The arrangement of…

Q: _6. Rylan's basketball team has 11 players. How many ways can his coach choose five starting…

A: Given;  1): No of player =11  To choose 5  starting players from the 11 players then nonof ways ?…

Q: How many ways are there to stack an​ ice-cream cone with 4 scoops if the choices are   a.…

A: For flavours must be different then once used flavour can't be used next time. So in first stack we…

Q: A Maryland automobile license plate consists of three letters followed by three numbers.  How many…

A: As per bartleby guidelines only one question should be answered once, please upload each question…

Q: A student club consists of 9 freshmen and 9 sophomores. • How many different six-person committees…

A: use permutation and combination find the solution

Q: How many ways are there to select an all-star team which includes all members from A, all members…

A:

Q: If 4 Maths books are selected from 6 different Maths books and 3 English books are chosen from 5…

A: Solution  Given That,  If 4 Maths books are selected from 6 different Maths books and 3 English…

Q: 2. The view of Sampaloc Lake is a very nice background to take pictures of. How many ways can 5…

A: Find the number of ways of arrangement

Q: How many ways are there to seat 6 different boys and 6 different girls along one side of a long…

A: Given that, there are 12 persons and 12 seats. 12 persons includes 6 boys and 6 girls. Therefore,…

Q: Among the eight nominees for two vacancies on a school board are four men and four women. How many…

A: Solution: It is given that there are 8 nominees for two vacancies on a school board. There are 4…

Q: 4. A photographer is taking a picture of a bride and a groom, together with six sponsors. How many…

A: 4) There are 8 people in total i.e., 6 sponsors and one couple. We are asked to find the number of…

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.