In a Sudoku tournament, 15 people qualified for the final round. If first, second, and third place medals are awarded based upon speed and accuracy, how many possible lists of award winners are there?

Q: At a furniture store, there a 4 different sizes of sofas, 7 different colors of fabric , and 8…

A: Given that, No.of  different sizes of sofas = 4 No.of different colors of fabric =7 No.of different…

Q: There are 12 people in a dinner gathering. In how many ways can they arrange themselves around a…

A: We use permutations and combinations. Number of ways to arrange n objects in n places is n! Number…

Q: If there are 57 cards in a deck and 12 are dealt to each student, how many 12 card possibilities are…

A: Combination Rule:The arrangement of r objects from n different objects is given by:

Q: Find the number of different ways that an instructor can choose 6 students from a class of 12…

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Q: In the Superfecta, one must pick the first four finishers of a horse race in correct order. If there…

A: For this question, assuming that all the horses were alive after the race, i.e. there were no…

Q: A coach had 21 people try out for the team, but only 13 people can make the team. How many different…

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Q: A speech class teacher is going to rank nine different speeches.  In how many different ways could…

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Q: The 14 teams in the local Little League are listed in the newspaper. How many listings are possible?

A: In this case, there are 14 teams in the local little league.

Q: How many different 8-letter arrangements are possible using the letters in the word PROCESS?

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Q: The University of Montana ski team has fifteen entrants in a men's downhill ski event. The coach…

A: In theory of combinatorics, the way of selecting r objects from n objects with regard to the order…

Q: At the bakery, a box of cookies is made by selecting four cookies from the six types of cookies –…

A: Formula nr = n!r!(n-r)! ; n ! = 1* 2* 3* 4*.. *n   Example : 3! = 1*2*3 = 6   Meaning : Number of…

Q: A photographer is asked to submit 7 photos from a collection of 14. How many ways can the photos be…

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Q: A student must answer 3 out of 5 essay questions on a test. In how many different ways can the…

A: A student must answer 3 out of 5 essay questions on a test. In how many different ways can the…

Q: A musician plans to perform 9 selections. In how many ways can she arrange the musical selections?

A: Given A musician plans to perform 9 selections

Q: In how many ways can 10 engineers be seated in a round table?

A: From the provided information, Total number of engineers = 10

Q: Out of the 12 people applying for a scholarship, a) how many ways can we select a group of five to…

A: N : number of students = 12 a) To select 5 people. = (12),(11),(10),(9),(8)  are the choices for…

Q: A college math department consisting of 10 faculty members must choose a department head, an…

A: Given, n=10 And we need to choose 3 faculty members from 10, here the order of 3 faculty member…

Q: If 11 people are to be seated in a row of 11 chairs, how many different seating arrangements are…

A: Given: 11 people are to be seated in a row of 11 chairs. The objective is to find different seating…

Q: If 15 people start a race, in how many different ways can the top 3 finishers be determined?

A: Permutation:   It  is an arrangement of objects in a definite order where the order is important.…

Q: At a movie festival, a team of judges is to pick the first, second, and third place winners from the…

A: Solution: From the given information, the number of films entered is 40 and a team of judges is to…

Q: Find the number of different ways that an instructor can choose 4 students from a class of 31

A: There are 31 students in a class room, out of 31 students 4 students can be chosen in 31C4 ways

Q: How many ways are there to select four pieces of fruit from a bowl containing apples, oranges,…

A: Observe the total numbers of ways  k distinct things form a set of n things is given by nk. Now…

Q: There are seven finalists for the Math contest, and medals will be given to the top three finalists.…

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Q: How many ways can seven people line up at a ticket window?

A: There are 7 people. n=7

Q: 10 officials were asked to sit in a round table. In How many ways can they be seated?

A: given  10 officials were asked to sit in a round table

Q: If 20 women are entered in the Miss Georgia contest, in how many different ways can the judges…

A: Given that 20 women are entered in the Miss Georgia contest.

Q: Ten jokes are listed in a magazine.   If the fourth joke from the magazine is​ excluded, in how…

A: There are 10 jokes listed in a magazine.Here 4th joke is excluded than find the number of ways…

Q: How many different patchwork quilts, four patches long and three patches wide, can be made from five…

A: Given: Five red and seven blue squares.   To determine: The number of different patchwork quilts…

Q: How many handshakes are required for a group of 15 people to shake everyone's hand?

A: Given information- We have given a group of 15 people. We have to find no. of handshake required to…

Q: How many arrangements are possible if all the letter E must be next to each other of the word…

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Q: In how many different ways can you arrange 8 figurines on a shelf?

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Q: How many different ways are there for the 10 people to stand in line to buy movie tickets?

A: How many different ways are there for the 10 people to stand in line to buy movie tickets?

Q: A bag contains 15 pieces of candy. In how many ways can four pieces be selected?

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Q: How many ways are there to select 47 cards from a standard deck of 52 cards?

A: To find: The number of ways to select 47 cards from a standard deck of 52 cards. Concept used: The…

Q: How many different five letter “words” can be made out of the letters in the word world?

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Q: How many arrangements are there using all the letters of the word cucumber?

A: There are 8 letters in the word cucumber. Among them: Letters Number of times appeared C 2 U…

Q: A mother duck lines her 12 ducklings up behind her. In how many ways can the ducklings line up?

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Q: How many arrangements are possible with 7 letters chosen from LAUREL MISSISSIPPI?

A: We have to find no of ways..

Q: How many ways can seven people be seated at a roundtable relative to the door of a room?

A: Number of people are = 7 The number of permutation of n elements in a circle is: P=n-1!

Q: How many different committees of three persons each can be chosen from a group of twelve people?

A: Combination: A combination is a grouping or subset of items. for a combination, the order not…

Q: What are all the ways in which the top 4 racers in a 20 person race can finish?

A: Introduction:In the given situation, the number of persons participated in the race is 20. The…

Q: A city soccer league has 8 teams.  In how many ways could the league assign first, second, and…

A: There are total 8 teams We have to pick 3 teams from those 8 teams.  Since it is ranking, so order…

Q: In a gathering, the host makes sure that each guest shakes hands with everyone else. If there are 30…

A: Given:Number of Guest = 30

Q: There is a town party in Pleasantville where 6 families of 3 people each get together. If one…

A:

Q: If 20 paintings are entered in an art exhibit, in how many different ways can the judges award a…

A: It is given that, 20 paintings are entered in an art exhibit. Then judge award the first prize to…

Q: At a movie festival, a team of judges is to pick the first, second, and third place winners from the…

A: The total number of films  =40  the number of ways to give first prize  is    =40 the number of ways…

Q: How many distinguishable ways can 3 people be seated around a circular table?

A: The answer is 3! = 6 different ways of  placing these three people in three distinct positions.

Q: 14 people try out for a basketball team, how many different ways are there to select 5 players if…

A: Given information: Total number of people who try out for a basketball team(n)=14. Number of…

Q: If a cube had been rolled 200 times, how many times would you expect a sum of 2 to be rolled?

A: From the table, we see that the sum of 2 rolled 3 times. In the table total number of rolls= 3+2+…

Q: many

A: