When I arrange the members of a marching band in rows of 2, 3, or 4, there is always 1 person left over. However, when I arrange them in rows of 5, the rows are all even. What is the minimum number of people in the marching band?

Q: I have 250 unique pairs of socks. If I want to have a pair of socks, what is the minimum number of…

A: Matching Pair: A matching pair is an experimental design where objects having the same…

Q: What is the minimum number of balls that we need to draw to ensure that we get at least 3 balls…

A:

Q: Consider 2 classes, the first with 5 students, and the second with 7 students. From this group of…

A: Given data 2 classes First with 5 students and second with 7 students 2 students need to be selected

Q: A pencil case has 400 colored markers: 200 blue, 120 red, 50 green, and 30 yellow. What is the least…

A: Given problem Given that   A pencil case has 400 colored markers . 200 blue 120 red 50 green 30…

Q: schedule is to be made with football teams. Suppose that 7 teams need to play with three other teams…

A: It's clear from the given problem that 7 teams play against three other teams. This leads to 7…

Q: The bus has left seats and right seats with the maximum seating capacity of 48 persons. If the right…

A: Maximum seating capacity = 48 Number of right seats of the bus = 23 Number of left seats of the bus…

Q: Assume that there are 3 pairs of black socks (çorap), 1 pair of pink socks, and 2 pairs of blue…

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Q: In a group of 100 people, each people needs to choose a number from 100 to 120. i)Prove that at…

A: Using the Pigeonhole principle we can prove the first statement. This principle states that if kn+1…

Q: find a set of smallest possible size that has both {3,4,7,8} and {1,5,6,9,10}

A:

Q: In a group of 100 people, each people needs to choose a number from 100 to 120. i)Prove that at…

A: Given: a group of 100 people, each people needs to choose a number from 100 to 120.

Q: A box contains 5 yellow, 8 green, 11 blue, 11 purple and 15 white balls. What is the minimum number…

A: Number of yellow balls = 5 Number of green balls = 8 Number of blue balls = 11 Number of purple…

Q: A box contains 18 red, 7 green, 11 blue, 21 yellow and 5 white balls. what is the minimum number of…

A: Given that a box contains 18 red, 7 green, 11 blue, 21 yellow and 5 white balls.

Q: 2) For a balanced incomplete block design, suppose you have 8 treatments and know that there can…

A: Given :-For a balanced incomplete block design, suppose you have 8 treatments and know that there…

Q: Six grocers sell an identical brand of coffee bean cans, in which each can is advertised as weighing…

A: GivenTotal number of grocer stores = 6Weight of coffee bean can = 4 ounces.One among the grocer is…

Q: There are six tutors, four juniors and two seniors, who must be assigned to the 6 hours that a math…

A: Part (a): It is given that there are 6 tutors, four juniors and two seniors. The math center is open…

Q: same

A:

Q: 4. Find the minimum number of students in a class to be sure that three of them are born in the same…

A: We have to apply the pigeon hole principle to solve this problem.

Q: A drawer contains 17 black socks, 17 white socks, 17 blue socks, and 17 brown socks. If the light is…

A: Let’s say that he has picked four socks. If he have already found a pair after two or three or four…

Q: Suppose that a coach must select 5 players to play on a basketball team. • The coach has 13 players…

A: The coach has 13 player to select from  And only 4 players can play center, so one of them has to be…

Q: Find the number m of ways that a class X with ten students can be partitioned into four teams A1,…

A:

Q: In a city each person earns at most $5000 per month and every house is occupied by at most five…

A: HERE Given  Maximum earnings of of person = $5000 Maximum person in one one house= 5

Q: • Suppose that a coach must select 5 players to play on a basketball team. • The coach has 12…

A: Given that there are 3 players who can play center. So we can choose center in 3 ways only.  When…

Q: If the light is off 17 plack socks and 17 white socks if the light is off and Matt reaches into the…

A: If he pulls 2 socks, then he might get one black sock and one white sock. So, n≠2

Q: Suppose the schedule at Pierce University has x mathematics courses and y computer science courses.…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: What is the minimum number of students, each of whom comes from one of 10 provinces who must be…

A: Let number of students that enrolled = n Number of provinces = 10 Number of pigeon holes = 10 Number…

Q: With a short time remaining in the​ day, a delivery driver has time to make deliveries at 5…

A: Given that, A delivery driver has time to make deliveries at 5 locations among the 9 locations.…

Q: rom a group of 7 men and 5 women, how many committees of size 3 are possible.  a) With no…

A: Given: No. of men=7 No. of women=5   Committee members=3

Q: A deli wants to line up all of their 20 pre-made sandwiches for display. There are 17 sandwiches…

A: We need to show that there will be 5 regular rolls in a row.

Q: Show that if any 14 numbers are selected from the set S = {1,2, 3, ..., 25}, %3D there are at least…

A: Given statement is If any 14 numbers are selected from the set S = {1,2,3,...,25}, there are at…

Q: What is the minimum number of cards that must be drawn from an ordinary deck of cards (52) to…

A: Given problem Given that   The minimum number of cards that must be drawn from a ordinary deck of…

Q: A bag contains 10 red marbles, 10 white marbles, and 10 blue marbles. What is the minimum number of…

A: From provided information; A bag contains 10 red marbles, 10 white marbles and 10 blue marbles. The…

Q: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that there…

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Q: Find the number of ways of getting at least a pair when randomly getting nine cards from a standard…

A:

Q: Suppose a n × n chessboard is missing two opposite corners. Prove that no matter what n is, you will…

A:

Q: If the mean of 5 positive integers is 15, what is the maximum possible difference between the…

A:

Q: drawer contains 17 black socks, 17 white socks, and 17 blue socks. If the light is off and Carol…

A:

Q: A drawer contains 22 black 22 white socks and 22 blue socks. If the light is off and Matt reaches…

A: Given information 22 Black socks 22 White socks 22 blue socks 3 types of socks are there He will…

Q: What is the maximum possible number of parasites for the

A: Here use given histogram to answer the question

Q: 2. The Hair Company offers two brands of shampoo: brand H and brand S. 100 people were surveyed and…

A: The Hair Company offers  two brands of shampoo name brand H and brand S total number of the people…

Q: Of all the books at a certain library, if you select one at random, then there is a 90% chance that…

A: Percent: It is the hundred part of the whole It is denoted by '%' The percentage can be written in…

Q: Twenty-five friends play golf in 5 groups of 5. Show that 6 is the minimum number of rounds they…

A: Given: Twenty-five friends play golf in 5 groups of 5.

Q: In a country, there are n farms and in each farm, there are at most 15 types of fruit trees. For any…

A: Use the data given to determine the answer. Use simple mathematics to determine the minimum number…

Q: Each of the 20 students learn exactly two of the three languages: English, French and German. 80% of…

A: Total number of students= 20 Number of students learn English= 80% of 20 = (80÷100)*20= 16 Number of…

Q: Assume that there are 2 pairs of black socks (çorap),3 pair of pink socks, and 5 pairs of blue socks…

A:

Q: What is the minimum number of students required in a discrete structures class to be sure that at…

A: As we have five grades: k=5 And the number of students: r=9 And we have to calculate: Nk=r N5=9

Q: Show that in a group of people there must be two individuals that have the same number of friends…

A: We make a proof by contradiction and use the pigeonhole principle.

Q: A restaurant provides a brunch where the omelets are individually prepared. Each guest is allowed to…

A: Let the restaurant offers n ingredients. When a person is choosing an ingredient for an omelet, then…

Q: Let [A1, A2], [B1, B2], [C1, C2] be 3 married couples who attended a concert.  Show that the number…

A: Consider that G is the group of females and B is the group of males.This two group of G and B can be…

Q: A company has 13 employees, and wants to create a team of 7 employees to work on a new project. Th…

A: Given : n = 13  r = 7

Q: Using the pigeonhole principle Assuming no one has more than 1,000,000 hairs on the head of any…

A: