Consider a room with 200 people. Let X be the number of days of the year in which there are exactly 3 persons having the same birthday. Let Y be the number of people having distinct birthdays.

Q: How many unordered selections of three elements can be made from the set {a, b, c, d, e, f}?

A:

Q: In a mall survey, 200 consumers were asked where they did their gift shopping; Macy’s, JC Penny’s,…

A: Let us denote M=Macy's, J=JC Penny’s, S=Sear's  Given that 40 people shopped at least at two…

Q: Construct NFA for 0*1*0*0 with three states.

A: Answer:

Q: How many elements of order 4 does A has.

A: To find Number of elements of order 4 does A6 has

Q: How many ways are there to choose two subsets A and B of [n] so that A ⊆ B, and |B| is even

A: Using logic of sets and subsets we will solve the problem. Using facts we will find a solution to…

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

A: There are two cases to consider:   Assume there is a someone at the party, who knows everyone else…

Q: How many possible results are there that A finished the first, B finished the second, and C finished…

A: SIX STUDENTS ARE SELECTED TO RUN 100 METER SPRINT. ASSUME THAT THEY ARE EQUALLY GOOD AND RESULT ARE…

Q: If set Z has 7 elements, how many subsets does it have?

A:

Q: Show that if there are 30 students in a class, then at least two have last names that begin with the…

A: We are given that there are 30 students in the class. We will assume that every student has first…

Q: Let the letters G and B denote a girl birth and a boy birth, respectively. For a family of three…

A: Let the letters G and B denote a girl birth and a boy birth, respectively. Given that a family has…

Q: In a group of people we have 7 football player 5 baseball player 1 who is both football player…

A: Venn diagram is diagrammatic representation of similarities and differences between two concepts .…

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

A:

Q: Let X ∼ Bin(n, p), and let Y = n − X. Show that Y ∼ Bin(n, 1 − p).

A: Here X follows Binomial with parameters n and p. Here, Y=n-X. Then Y takes the values n-0, n-1,…

Q: at a school assembly,4 out of the first 10 students were wearing spirit wear. Based on this…

A: Total number of student at school assembly = 500

Q: Suppose n(ANB) = 3, n(AUB) = 38, and n(A) = 18. Use a Venn diagram to determine n(B). n(B) = %3D

A: Given n(A∩B) = 3,  n(A∪B) = 38andn(A) = 18

Q: Describe the possible inputs of S(n) using words.

A: The possible inputs for S are the numbers on a dice

Q: ist of at least one woman is

A:

Q: Assume that there are 9 pairs of shoes in a closet. How many single shoes must you choose at random…

A: Suppose the first shoe is chosen at random and after that 8 different shoes are chosen. Then the…

Q: Assume that you are assigning one of 12 available lockers to each of the 8 players on the team. In…

A:

Q: There are m months in a year, w weeks in a month and d days in a week.How many days are there in a…

A: Number of days in 1 week = d Number of days in w weeks = d×w…

Q: Find the number of different signals that can be made by arranging at least three flags in order on…

A: find the number of different signals that can be made by arranging at least three flags out of 6

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: Balls are numbered 1 through 10 (including 1 and 10) in an urn. 3 are drawn simultaneously and at…

A:

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: List the elements of set D = { x:x є N, x is a multiple of 5} where N= {1, 2, 3, ...}.

A:

Q: In a meeting, we have  25  people who go to school 30 people who have part time job 45 people…

A:

Q: Consider all subsets of size four of the set {1, 2, ..., 20}. How many of them have a nonempty…

A: Given: It is given that by considering that all the subsets of size four of the set{1,2,....20} The…

Q: If a set S has n > 3 elements, how many subsets of S have less than n – 1 elements?

A: Apply the simple logic of Permutation & Combination.

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: State whether each arrangement represents a permutation or a combination.   a. 8 people seated…

A: Arrangement classification- Permutation or Combination

Q: Consider the word TORTOISE. Count the number of arrangements of this word (a) such that no two…

A: Consider the given word TORTOISE. The objective is to count the number of arrangements of this word:…

Q: There are n balls in the urn , of which (n-1) balls are marked   with the number 1 , and the last -…

A:

Q: When testing for current in a cable with eleven color-coded wires, the author used a meter to test…

A: The combination formula is shown below. Here, n represents the total number of objects and r…

Q: Suppose n(ANB) = 3, n(AUB) = 36, and n(A) = 14. Use a Venn diagram to determine n(B). B n(B) =

A:

Q: list all the possible sets of Cities thot Charlie Con

A:

Q: Let S := {l, a, t, e, r, a, l}. How many subsets does S have?

A: Given: S = {l, a, t, e, r, a, l} Here, number of elements is n = 7.

Q: Let n(A) denotes the number of elements in set A. If n(A) =p and n(B) = q, then how many ordered…

A: Given that: n(A)=p, and n(B)=q

Q: andomly selected from a

A: we have given a sample of 6 measurements was randomly selected from normally distributed population…

Q: find the subset of (E, B,T,*)

A:

Q: er

A: To find all the permutations of the 4 objects a ,b, c, and d, taken 3 at a time.

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

A: This is an application of pigeon hole principle. According to pigeon hole principle, if there are n…

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: Suppose we want to choose 5 objects, without replacement, from 15 distinct objects.

A: Given data: The total numbers of objects are n=15. The numbers of objects choose is r=5. (a) Write…

Q: Prove that among any group of people, there are always two people with the same number of friends…

A:

Q: by each participant is presented here.

A: Let X1 be the random variable such that jail sentence recommended by the participants in group 1. M1…

Q: Compute 0.5x for the following set of n = 7 values. x1 = 4, x2 = 19, x3 = 18, x4 = 10, x5 = 16, x6 =…

A: Solution: From the given information, n=7 and the set of values are

Q: An un contains cards numbered 1.2...100. Let X be the least number on the 50 cards drawn randomly…

A: Given problem is :

Q: For the experiment in which the number of pumps in use at a single six-pumps gas station is…

A: 1.Look elements of both set A and B carefully 2. Cancel all the elements which is found similar in…