Show that among any 4 n−1 people, there are either some n of them who mutually know each other, or some n who mutually don’t know each other.

Q: How many outfits can be made from 4 pairs of slacks, 5 shirts, and 3 ties, if one selection from…

A: First decide on a pair of slacks.For that there are 4 different choices.Now for each of those…

Q: How do I prove that if a, b, and c are integers with c not equal to 0 then ac = bc => a = b?

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Q: Assume that the committee consists of 10 Republicans and 5 Democrats. A subcommittee consisting of 5…

A: Given Information: Assume that the committee consists of 10 Republicans and 5 Democrats. A…

Q: Suppose that 8 men give their hats to a hat-check person. How many ways that the hats can be given…

A: The number of men who give their hats to a hat-check person is

Q: If there is a bird in every branch, there will be an excess bird not on the branch but if there will…

A: Here, it is given to us that: There is a bird for every branch, and if each bird sits on one branch…

Q: A car traveling along a street needs to pass through 4 intersections with traffic lights. If each…

A: Introduction: It is required to find the probability mass function of pmf of X.

Q: How many five-digit numbers are there for which each digit is either equal to both adjacent ones, or…

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Q: Assume that there are 10 girls and 12 boys in the neighborhood club, and a team of 7 is to be…

A: Assume that there are 10 girls and 12 boys in the neighborhood club, and a team of 7 is to be…

Q: in how many ways can 5 starting positions on a basketball team be filled with 12 men who can play…

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Q: Seven out of every ten monkeys in a zoo are smarter than the zookeepers. If there are 40 monkeys in…

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Q: Prove that at a party where there are at least two people, there are two people w know the same…

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Q: Show that if a1,: a2., an are integers that are not all 0 and c is a positive integers, then…

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Q: How many 5–digit (decimal) integers are there with none of the digits repeated?

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Q: How many positive integers less than 10000 are there which contain at least one 2 or at least one 3…

A: The objective is to evaluate the number of positive integers less that 10000 that contain at least…

Q: Assume that there are 8 girls and 12 boys in the neighborhood club, and a team of 6 is to be…

A: Given information: Number of girls, g = 8 Number of boys, b = 12 A team of 6 is to be selected. It…

Q: Prove that among 7 positive integers, there are always two integers such that either their sun or…

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Q: 7. For n ≥ 1, verify that 12+32 +52 ++ (2n- +3²+5² · + 2n-1)² = (2n+1) 3

A: Ans : page 1:Ans page 2:

Q: We select 38 even positive integers, all less than 1000. Prove that there will be two of them whose…

A: Introduction: Pigeonhole principle: The Pigeonhole Principle is a fundamental principle in…

Q: d = (a, b, c).

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Q: Assume that there are 10 girls and 8 boys in the neighborhood club, and a team of 8 is to be…

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Q: Let A=[-1,7[,8={-1,3,10,12} and C={}}. Then (A-B) UC= *

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Q: Assume that there are 70 students: 36 who enjoy tennis, and 13 who enjoy swimming but not tennis.…

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Q: We select 38 even positive integers, all less than 1000. Prove that there will be two of them whose…

A: Given statement is Here we can select 38 even positive integers all are less than 1000. let…

Q: MK18. Show that in any set of 9 integers chosen from the set {2,3, 4, ... , 21, 22}, there are at…

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Q: Suppose you break your piggy bank and scoop up a handful of 22 coins (pennies, nickels, dimes and…

A: a) We will prove this using contradiction Suppose we have 5 coins of each denomination. So, we have…

Q: prove that the sum of four consecutive integers is even.

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