How many people must be selected to guarantee that at least 4 have a birthday in the same month?

Q: Assume the cards are drawn sequentially and without replacement. (permutations) In how many ways…

A: Given data, given that 5 Spades can be drawn from a standard deck of 52 cards. The cards are drawn…

Q: Eight horses are entered in a race. In how many ways can the horses finish considering that at least…

A: Permutation: The number of different arrangements of ‘r’ elements from a set of‘n’ elements is…

Q: 2. Civil Engineers at a large convention are offered 6 construction tours on each of 3 days. In how…

A: Given : Number of tours = 6 Number of days = 3

Q: Suppose that in a certain association, there are 12 elected members of the Board of Directors. In…

A:

Q: Suppose 84% of students chose to study Spanish their junior year, and that meant that there were 378…

A: Then,

Q: If a phone company sends a random 6-digit number to customers to activate their phone, how many…

A: Consider a problem in which there are n vacant inline spots, each spot is to be filled by any of the…

Q: How many days must be selected from the year to guarantee that at least 4 falls in the same…

A:

Q: 5. How many 2-permutations are there of a set of eight objects?

A: We know that,  The formula pf permutations is,  nPr = P(n, r) = n!/(n-r)!

Q: How many permutations π of [10] satisfy π^5 = 1?

A: The given set is 10=1,2,3,…,10. Therefore any permutation π of 10, is bijective function from the…

Q: How many different license plates are available if each plates contains a sequence of three letters…

A: There are 26 letters (A to Z) and 10 digits (0 to 9). Given that, the license plates consist of 3…

Q: Be able to demonstrate the fact that at least 10 of the 64 days selected must occur on the same…

A: let we have selected 64 daysThen day 1 is any one week day from 7weekdaysLet day 1 is weekday xAfter…

Q: If three alphabets are to be chosen from A, B, C, D and E such that repetition is not allowed then…

A: In question, Given that A, B, C, D and E are 5 alphabets then three alphabet are chosen from them…

Q: 7. In a group of 30 people, must at least 3 have been born in the same month? Why?

A: To show that in a group of  30 people, must at least 3 have been born in the same month.

Q: How many numbers must be selected from the set {2,4,6,8,10,12,14,16,18,20} to guarantee that at…

A: Use the principle of inclusion and exclusion to solve this problem, as in next step.

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: How many numbers must be selected from the set {1, 2, 3, 4, 5, 6} to guarantee that at least one…

A: To find  How many numbers must be selected from the set {1, 2, 3, 4, 5, 6} toguarantee that at least…

Q: 6. How many different 3-digit identification tags can be made if the digits can be used more than…

A: Note- Since both are different questions, so according to our policy we can answer only one…

Q: Assume that you select digits from the set {2,3,5,7} to form a number between 20 and 700. (1) How…

A: The given set of digits is 2,3,5,7 and the range of numbers is 20 to 700. There would be 2 digit…

Q: If 162 strings of lights were disposed of last week because they were deficient, how many strings of…

A:

Q: How many four-digit passwords can be made from the digits 0 to 5, if digits can be repeated?

A: From 0 to 5 there are 6 digits.  Given that the digits can be repeated. This means for each digit…

Q: How many 15-bit strings contain exactly seven 1's?

A: Out of 15 strings one must pick 7 of them to contain 1’s and other 8 will contain 0’s.

Q: How many different signals can be made using AT LEAST 4 distinct flags if there are 7 different…

A: Solution:  Different signals can be made using; AT LEAST 4 distinct flags if there are 7 different…

Q: Consider the numbers 2, 4, 5, 7 and 8. If repetition is not allowed, how many three digit numbers…

A: Solution To make the 3 digit number we will use permutation.

Q: How many 4-permutations are there of a set of six objects?

A:

Q: Show that if there are 8 people in a room, then at least two of them must have been born on the same…

A: There are 7 days in a week.  So we can have 7 people who can have different birthdays from Sunday to…

Q: How many 4-letter strings of upper- and/or lowercase letters are there that contain at least two…

A: To determine the number of 4-letter strings of upper and /or  lowercase letters are there that…

Q: Each customer in a certain bank has a PIN number, which is a sequence of four digits. Show that if…

A:

Q: PLEASE HELP, i really need to understand these questions before my finals. pleaseee?

A: The Pigeonhole Principle:  If there are n+1 objects and it is required to place then in n boxes then…

Q: A TV game show selects four contestants from an audience of 26 people. If the same 26 people showed…

A: Given: Total number of people=26Number of people selected=4 The permutation formula is applied when…

Q: How many strings of 7 decimal digits are there, such that at least one of the digit is odd?

A: There are total 10 decimal digits, among which 5 are odd. Since repetition of digits is allowed,…

Q: Assume the cards are drawn sequentially and without replacement. In how many ways can 3 diamonds be…

A: Given information- We have given that 3 diamonds be drawn from a standard deck of 52 cards. The…

Q: Each employee at a large company is to be issued an ID number; the ID number is to consist of one…

A: Digits sequence '000' taken as valid ID, if not one less from the answer below. There is no such…

Q: A coin is flipped 7 times in succession. In how many ways can at least four heads occur?

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

Q: How many collections are possible? How many of these collections contain HPQ but not SAGE? How many…

A: Given, Purchasing 3 tech stocks and 2 health care stocks from those stocks To find The number of…

Q: Prove that among 100 people, at least 9 were born in the same month.

A: We have a group of 100 people. We need to prove that at least 9 were born in the same month. We will…

Q: a committe of four people is to be chosen from a nine member group to represent the group on an…

A: a committee of four people is to be chosen from a nine member group to represent the group on an…

Q: How many 6-permutations of [15] have their digits in increasing order?

A: Permutation is a technique to obtain the possible arrangements of listed items in a linear order.…

Q: how many committes of seven with a given chairperson can be selected from 13 persons?

A:

Q: How many people are needed to guarantee that at least two were born on the same day of the week and…

A: There are 7 days in a week and 12 months in a year.

Q: A lock has a code of 3 numbers between 1 and 10. If no numbers in the code are allowed to repeat,…

A: Answer - A  lock has a code of 3 numbers between 1 and 10. {1, 2, 3, 4, 5, 6, 7, 8, 9,10 }…

Q: A firm is considering expanding into 5 of 14 possible cities. How many different groups of 5 cities…

A: The combination formula is nCx = n! /(n-x)! x!

Q: Consider a bracelet that is made up of 12 different charms. In how many ways a designer can design…

A: AS PER BERTLEBY GUIDELINES, WE ARE ALLOWED TO SOLVE ONLY ONE QUESTION WHEN MULTIPLE QUESTIONS ARE…

Q: How many different calendars are possible for a year?

A: Here Given  There is two type of years LEAP and NON LEAP Year

Q: Five cards are selected out of 52. In how many different ways can this be done if: they contain at…

A: If ways of occurrence of 1st event is m  And ways of occurring of the second event is n  And if both…

Q: 11 Given the digits 6, 7, 8, 9, a. How many four number digits can be formed if there's no…

A: Given digits are  6, 7, 8, 9 each parts are solved below.

Q: 2) A class has 25 students. Each day, three students are chosen to present their work at the board.…

A:

Q: 1. Will there be at least five people who celebrate their birthday in the same month Yes No

A: Note- Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

Q: How many three-letter code words can be constructed from the first ten letters of the Greek alphabet…

A: We have to find how many three-letter code words can be constructed from the first ten letters of…

Q: A computer access password consists of from three to ten letters chosen from the 28 in the Arabic…

A: The part b of the can we solved by using the permutation.

Q: How many six-number combinations can be generated from the numbers from 1 to 42 inclusive, without…

A: Given information: A 6 number combination is to be generated. The possible numbers are selected…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.