Answered: Prove that at a party where there are…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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4. Dennis and Grace got married today and are having a photo session together. At a photo session Dennis is on the left and Grace is on the right. There are 12 men and 10 men woman taking the photo. However, unfortunately only 10 people can take pictures, namely 5 person next to Dennia and 5 people next to Grace. Dennis doesn't want any men in next to Grace and vice versa Grace does not want any woman beside Dennis. Count how many different possible photos there will be. Notes:● A photo is considered different if there is a different sequence or person in eachposition.● Assume that your partner will always be in the middle position.● The composition of women and men does not have to be the same (there can be 8 men and 2 women participating in the photo) Solve in 45 minutes thank u
A deck of 52 cards is equally dealt to 4 players. Find the number of ways to distribute the cards so that the cards for each player are of the same colour. [Note: in a deck of 52 cards, 26 of them are red (,0), and 26 of them are black ,+).]
Suppose you are dealt a 5-card poker hand and your first 2 cards are both twos. How many ways are there to complete your hand such that you end up with no better than a 3 of-a-kind?
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Phoenix is a hub for a large airline. Suppose that on a particular day, 8,000 passengers arrived in Phoenix on this airline. Phoenix was the final destination for 1,600 of these passengers. The others were all connecting to flights to other cities. On this particular day, several inbound flights were late, and 410 connecting passengers missed their connecting flight and were delayed in Phoenix. Of the 410 who were delayed, 85 were delayed overnight and had to spend the night in Phoenix. Consider the chance experiment of choosing a passenger at random from these 8,000 passengers. Calculate the following probabilities. (Round your answers to three decimal places.) (a) Calculate the probability that the selected passenger had Phoenix as a final destination. (b) Calculate the probability that the selected passenger did not have Phoenix as a final destination. (c) Calculate the probability that the selected passenger was connecting and missed the connecting flight. (d) Calculate the…
N5 Suppose that you have a group of 10 people (where any two people are either friends or enemies) and one person has at least 6 enemies. Prove that there are either three mutual friends or four mutual enemies.
Show that in a group of five people (where any two people are either friendsor enemies), there are not necessarily three mutual friends or three mutualenemies.
How many of these students like Haydn and exactly one of the other two?
In a survey of 252 professional athletes, it was found that 119 of them owned a convertible, 122 of them owned a giant screen TV, and 115 owned a sporting goods store. 21 owned a convertible and a store, 44 owned a TV and a store, and 73 owned a covertible and a TV. 13 owned all three items. How many athletes did not own any of the three items? How many owned a covertible and a TV, but not a store? How many athletes owned a convertible or a TV? How many athletes owned exactly one type of item in the survey? How many athletes owned at least one type of item in the survey? How many owned a TV or a store, but not a convertible?
If you have 12 boxes then how many balls do you have to put randomly into the boxes in order to guarantee that some box will contain at least 4 balls?
After an earthquake, 32 homes in a remote area were checked by public safety officers before nightfall. They found that 22 of the houses had no gas, including 10 houses whose own gas lines were damaged. (A house loses its gas service if it has damage to its own line or if there is damage to the feeder line.) Of those houses that lost their gas, only 4 did not lose their electricity. Twenty-four houses in all had no electricity, the same number of them lost only their electricity as those that both lost electricity and had damage to their gas lines. How many of the houses checked did not lose either gas or electricity, and how many lost only their gas service! Students, draw anywhere on this slide!
A survey of 300 adults found that during the last year, 82 purchased apples but not strawberries, 91 purchased oranges but not apples, 50 purchased strawberries but not apples or oranges, 32 purchased strawberries and oranges, 22 purchased all three, and 178 purchased strawberries or apples. Fill out a Venn diagram and determine how many of the adults surveyed did not purchase any of the three fruits.

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Prove that at a party where there are at least two people, there are two people who know the same number of other people there.