(b) Use the Pigeon Hole principle explains the following statement with proper justification. In any group of n persons, there are at least two persons having the same number of friends.

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A: Here use venn diagram

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A: Probability of getting a tail =1/2 Probability of getting  a white marble(when coin flips tail)=2/3…

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A: Note: As per Bartleby guidelines, I can answer only maximum 3 sub-parts. So, kindly repost the…

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A:

Q: The average age of the members of a country club is 54 years old. If there are ten 36-year-olds,…

A: Let the age of 20 other members be x years. Now  Age of 10 members=36 Age of 50 members =60 Total…

Q: 1. What is the converse of the following statement? If you are a quarterback, then you are on the…

A: Given statement is, If you are quarterback, then you are on a football team.

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A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 7. A woman has 12 close friends. Find the number of ways she can invite 6 of them to dinner where:…

A:

Q: In how many ways can a group of five girls and five boys be lined up so that: (a) all the girls…

A: Permutation: A permutation of a set is defined as an arrangement of its members into a sequence or…

Q: In a group, 25 people like tea or coffee, of these 15 like tea and 6 like both coffee and tea. How…

A: ∗ formulanA∪B=nA+nB-nA∩BLet C denote the set of people who like coffeeand T denote the set of people…

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A:

Q: In how many ways can 3 boys and 3 girls be seated at a round table if a.     without restriction b…

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Q: Consider a group of 7 people divided among 5 rooms. 1. Are we guaranteed at least room with more…

A: statement of pigeon hole principle:- let m be the pigeons and n pigeon halls, m>nthere is at…

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A: The formula for combination is C(n, r) = n! / [r! (n – r)!] = [n (n – 1) … (n – r + 1)] / r!.…

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A: Since you have posted multiple sub-parts, we will solve the first three sub-parts for you. To get…

Q: se pigeonhole principle 1. A drawer holds a dozen unmatched brown socks and a dozen unmatched…

A:

Q: OIn a group of 37 people, at least 4 people must have been born in January. OIn a group of 8 people,…

A: If there are n people who can shake hands with one another (where n > 1), the pigeonhole…

Q: In how many ways can they line up so that no two geese are standing next to one another? (There is…

A: There are 10 ducks and 6 geese.

Q: There are 10 guests (1 is the host) in a conference. In how many ways can he accommodate his guests…

A: total number of guest =10 number of ways  person can arrange in circular table is (n-1)!

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Q: 2. Nine runners are entered in a 100-meter dash for which a gold, silver, and bronze meda will be…

A: Solution: Total number of runners = n= 9  Number of medals = Gold, Silver and Bronge= r= 3

Q: In how many ways can you invite one or more of your five friends to a party?

A: There are total 5 friends available among which 1 or more than 1 friends can be invited to the…

Q: A group of 30 people have been trained as astronauts to go on the first mission to Mars. How many…

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Q: 7.The 11colleges of interest to a high school senior include that are expensive​ (tuition more than​…

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Q: In a lottery, there 250 prizes of $5, 50 prizes of $25, and ten prizes of $100. Assuming that 10,000…

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Q: A baseball tgam has 16 players. Suppose that the team has three star players: Ryan, Glenn and Manny,…

A: Given: The first 3 places are already fixed to Ryan, Glenn, and Manny.

Q: 8. A woman has 10 close friends. Find the number of ways in which she can invite 4 of them dinner if…

A: 18) A woman has 10 close friends. To find the number of ways in which she can invite 4 of them to…

Q: 3. How many possible ways to assign a room for each of the 5 students, suppose we have 8 rooms…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: 4. You are dealt 5 cards from a standard deck of 52 playing cards. In how many ways can you get…

A: In a pack of 52 cards there are 4 suits and each suit has 13 cards so there are 3 similar cards to a…

Q: In a certain group of 50 students at Hogwarts School of Wizardry, only 15 students are wearing caps…

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Q: In a survey, 105 people were asked if they believed in UFOS, ghosts, and Bigfoot. 12: ghosts and…

A: *concept:- draw Venn Diagram.

Q: The five most common words appearing in spam emails are shipping!, today!, here!, available, and…

A: Since you have posted question with multiple sub-parts, we will solve first 3 sub-parts for you. To…

Q: 2. There are 102 students in John's freshman seminar class at SUNY Oneonta. The professor tells her…

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Q: A camp counselor and eight campers are to be seated along a picnic bench. In how many ways can this…

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A: Given data is: The conditions are:

Q: The following statements represent the dgrees of ten students in the subjects of democracy x and…

A: Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have…

Q: 4. (a) In a group of 8 people, some of them shake hands. Is it possible that everyone shaked hands…

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Q: company’s CEO has 8 people reporting directly to her, and she wants to select 2 to attend the grand…

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Q: A total of 60 students have taken the discrete math exam which provided 3 questions A, B, and C.…

A: It is an important part of statistics . It is widely used .

Q: 3. A donut shop has donuts in the following five varieties: glazed, powdered, cinnamon, blueberry,…

A: given: donuts of each variety having 5 varieties. So, total 13*5 = 65 donuts  a). choosing 13 donuts…

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Q: Which of the following groups of students at Oxnard College would be smallest? Students that are…

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Q: A shipment of 12 television sets contains 3 defective sets. In how many ways can a hotel purchase 5…

A: It is given that the, A shipment of 12 television sets contains 3 defective sets. Number of…