1. A restaurant is preparing a large round table with 2 +1 seats (the seats are unla- belled). The waiter has n + 1 red napkins and n blue napkins. How many visually distinct ways are there for the waiter to place the kins around the table? Give a combinatorial proof that your solution is correct. nap-

1. A restaurant is preparing a large round table with 2 +1 seats (the seats are unla- belled). The waiter has n + 1 red napkins and n blue napkins. How many visually distinct ways are there for the waiter to place the kins around the table? Give a combinatorial proof that your solution is correct. nap-

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Please help solve this question into details for me. I want to use it to understand the concept of permutation and combinations. Thanks a lot. For this Big Problem, we’re going to investigate the different combinatorial formulas tofigure out why they are the way they are. Using Zoom! (1) Suppose you are organizing a Zoom meeting and invite ten people. You don’t knowwho all is coming so you watch people sign on one at a time. How many possibilitiesare there for the first, second, and third people to sign on? (2) What formula did you use for question one, and why? (3) Suppose you are running late so by the time you log on three people have alreadyarrived. How many possibilities are there for which three people are logged on? (4) What formula did you use for question three, and why? (5) You know that Person A, Person B, and Person C logged on before you but you don’tknow who came first. How many possibilities are there for the order of A, B, and Cto have signed on before you? (6) What…
A baseball fan purchases 6 red “Home Game” shirts and 10 blue “Away Game” shirts. For part (b), assume all the shirts are identical except for their color (b) How many ways are there to hang all of the shirts on the clothesline if we don’t want 2 red shirtsnext to each other?
Nine IU South Bend students are going on a trip to Indianapolis for a Clots game. Go Colts! (a) They will seat in a row. In how many ways can they seat if Josh, Mark and Mary will sit together? (b) They will travel with three cars that hold 2, 4, and 5 people, respectively. All of them can drive. Find the number of possible ways to allocate 9 people to 3 cars that each car has at least one person (each car has to have a driver) (i) if the allocations are to the cars only (disregard the seats in the car). (ii) if the allocations are to the seats.
A) When does combinatorial explosion occcurs? B) What do people do to avoid this from happening when making decisions or solving problems?
Please help me. Why is b is wrong? Should it be 10! - 2! ?
Assume that the committee consists of 7 Trolls and 7 Ogres. A subcommittee consisting of 7 creatures is to be selected. (1) How many such subcommittees are possible if each subcommittee must contain exactly 4 Trolls and 3 Ogres? (2) How many such subcommittees are possible if each subcommittee must contain at least 1 and no more than 3 Ogres?
In a gaming conference attended by 80 people, 35 plays Valorant, 20 plays DoTA, 15 plays Genshin Impact. 5 plays both Valorant and Genshin Impact, 10 plays both Valorant and DoTA, 7 plays DOTA and Genshin Impact, and 4 plays all 3 games. Find the number of people who plays at least one of the games stated.
Twenty-one girls and twenty-one boys took part in a mathematical compe- tition. It turned out that (a) Each contestant solved at most six problems, and (b) For each pair of a girl and a boy, there was at least one problem that both of them solved. Prove that there is a problem that was solved by at least three girls and at least three boys.
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If n(A) =7, n(B)= 8, and n(A intersection B)= 6 what is n(A Union B)?
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Discrete Math: Q# 1. How many strings of 9 letters can be created if the first and last letter must be the same? Is this 26^8 * 25? Q#2. How many ways can a president, a vice-president, and a treasurer be chosen from a committee of 20 people? Is this 1140? I got this using the combinatorics definition using P(20,3)=20!/3!(20-3)1 Or is it 20!/(20-3)!=6840? I'm not sure which one to use. Q#3. How many numbers are there between 5 and 157 that are divisible by 3? Is this 52-3+1=50? I'm just going over some practice questions and want to make sure I'm on the right track. Thanks :)