There are n friends who eat out at a fancy restaurant, with each person ordering a unique appetizer. Unfortunately, the server at this super-expensive restaurant didn’t write down who ordered which dish. To avoid embarrassment, the server randomly placed an appetizer in front of each person, hoping that they guessed correctly. Assume all n! permutations are equally likely. Determine the expected value of the number of people who received the appetizer they ordered

There are n friends who eat out at a fancy restaurant, with each person ordering a unique appetizer. Unfortunately, the server at this super-expensive restaurant didn’t write down who ordered which dish. To avoid embarrassment, the server randomly placed an appetizer in front of each person, hoping that they guessed correctly. Assume all n! permutations are equally likely. Determine the expected value of the number of people who received the appetizer they ordered

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...

See similar textbooks

Similar questions

Last semester in a business fraternity, 30% of the members were on the Dean's List and 15% of the members were on academic probation. If being on the Dean's List and being on academic probation are mutually exclusive events, find the percent of members who were neither on the Dean's List nor on academic probation.
A class contains 8 boys and 7 girls. The teacher selects 3 of the children at random and without replacement. Compute the probability that the number of girls selected exceeds the number of boys selected.
The probability that a house in an urban area will be burglarized is 5%. If 85 houses are randomly selected, what is the probability that none of the houses will be burglarized?
A group of five students went to a hotel with 10 upper floors and a ground floor. The students simultaneously enter the elevator at the ground floor. The students choose their exit floors independently of each other. Determine the probability that they are all going to different floors when each student randomly chooses one of the 10 floors as their exit floor.
At the beginning of the semester, each of the 5 students in a class selected a nickname. Unfortunately, the instructor forgot how the given names of {A, B, C, D, E} matched up to their nicknames:{a, b, c, d, e}. Determine the probability that the instructor got none of the five matches correct.
There are 400 brunets, 150 blonds, 200 brown-haired people and 50 red-haired people. Find the probability that among randomly selected 32 people there are 16 brunets.
A teacher will pick 1 student at random from 20 for the lead in a play. What is the probability of a student, Jo, of winning?
A jar contains 2 red marbles, 8 green marbles, and 5 blue marbles. What is the probability that you draw 3 green marbles in a row if you do replace the marbles after each draw? = What is the probability that you draw 6 blue marbles in a row if you don't replace the marbles after each draw?
A magazine subscription service is having a contest in which the prize is 180000. If the company receives 3 million entries, which is the expection of the contest?
you get a color ball either red, blue or green when you buy a pack of chocolate. You can only buy 2 packs of chocolate each time. What is the expected number of 2 packs to buy for you to get all three color balls?
A team of five persons are to be selected from a group of 4men, 3 women and 3 childrens. What is the probability that team comprises of exactly two women?
A committee of 5 people was selected from 6 men and 9 women. If the selection process is random, what is the probability that the committee consists of 3 men and 2 women?